chapter 24, 25, 26

Suppose the oil had an index of refraction of 1.50. What would the minimum thickness ttt be now?

125

What is the longest wavelength λλlambda of light that will exhibit constructive interference at normal incidence? The keratin layers are thin enough that you can think of them as representing the surfaces of a 200-nmnm "film" of air.

400 nm

PART B If the correcting lenses will be contact lenses, what focal length lens is needed ?

64.1 CM

part C Find the height of the image of the insect.

=-29 cm

What type of lens (converging or diverging) is needed to correct his vision?

A converging lens is needed to correct his vision.

Which of the following scenerios fits all of the criteria for the two-source interference equations to be valid?

An observer stands on a road that runs five kilometers away from the two synchronized transmitting towers for a radio station.

What is the power of his eye in diopters when he focuses on the photo?

D =42.5dioptersdiopters

part D If the mirror is immersed in water (of refractive index 1.33), what is its focal length?

D) focal length does not change even if we immersed in water =17.2

part B Joe's eyes are focused on the tree, so the squirrel and the mountain appear out of focus. This is because the image of the squirrel is formed ______ and the image of the mountain is formed _____.

behind the fovea / between the lens and fovea

What is the distance ddd between points A and B?

d =0.500wavelengths

part D If two convex lenses identical in size and shape are manufactured from glass with two different indices of refraction, would the focal length of the lens with the greater index of refraction (lens 1) be larger or smaller than that of the other lens (lens 2)? part E If lens 1 from Part D were placed in exactly the same location as lens 2, would the image produced by lens 1 be larger or smaller than the image produced by lens 2?

smaller part E smaller

If this coating is too thin to stand up to wear, what other thicknesses would also work? Find only the three thinnest ones.

t2, t3, t4 =198,298,397

Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 10.0 cm part b Calculate the size of the image.

-1.62

If the cornea were simply a thin lens in air, what would be its power in diopters?

-4.61

The largest refracting telescope in the world is at Yerkes Observatory in Wisconsin. The objective lens is 1.02 mm in diameter and has a focal length of 19.4 mm . Suppose you want to magnify Jupiter, which is 1.38×105 kmkm in diameter, so that its image subtends an angle of 1212∘∘ (about the same as the moon) when it is 6.28×108 kmkm from earth. What focal-length eyepiece do you need?

0.489 m

Examining your image in a convex mirror whose radius of curvature is 24.2 cmcm , you stand with the tip of your nose 11.0 cmcm from the surface of the mirror. What is its magnification?

0.524

A converging lens forms an image of an 7.50 mmmm -tall real object. The image is 11.5 cmcm to the left of the lens, 3.40 cmcm tall, and upright. Where is the object located?

2.54

part c What is the overall angular magnification of the microscope?

-249

What is the width of the first bright fringe on either side of the central one?

0.05

What is its magnification?

0.524

Why are the two-source interference equations not valid for light from an incandescent bulb that shines onto a screen with a single slit, and then the light shines onto a screen with two slits in it and the light from the two slits finally shines onto a nearby screen? not monochromatic sources incoherent sources observed from a distance similar to or smaller than the separation between the sources

1 and 3 only

Which answer best describes the image seen through the eyepiece of the telescope?

a virtual and enlarged image

The location of the object to be viewed far away results in what sort of image?

an image at the focal point of the objective

(Figure 1) shows an object and its image formed by a thin lens. Assume that LLL = 15.2 cm and y = 3.30 mm What is the focal length of the lens?

f =53.7cm

part b What is the magnitude of the linear magnification produced by the objective?

m1 =-19.9

A lens placed at the origin with its axis pointing along the x axis produces a real inverted image at x=−24cmx=−24cm that is twice as tall as the object. part H What is the image distance?

s'= 24 cm

A convex spherical mirror has a radius of curvature of 11.0 CM .

s′ =-5.47cm

(Figure 1) shows an object and its image formed by a thin lens. Is it real or virtual?

virtual

A tank whose bottom is a mirror is filled with water to a depth of 20.7 cm . A small fish floats motionless 8.00 cm under the surface of the water. What is the apparent depth of the fish when viewed at normal incidence to the water? part b What is the apparent depth of the reflection of the fish in the bottom of the tank when viewed at normal incidence? Express your answer in centimeters. Use 1.33 for the index of refraction of water.

(1/1.33)*8 cm= 6.02 Part B 2* 20.7 - 8= 33.4 (1/1.33)*33.4= 25.11

Ordinary glasses are worn in front of the eye and usually 2.0 cmcm in front of the eyeball. Suppose that a nearsighted person with a far point of 120 cmcm uses ordinary glasses to correct her vision of faraway objects. What eyeglass power will give her a sharp image of objects at infinity? (Do not ignore the distance between the eye and the glasses.)

-0.85

Finally, use the magnification to find the height of the image y′.

-12

Calculate where the image should be.

-17.1

Find the magnification m, using s and s′.

-2

A student's far point is at 23.0 cmcm , and she needs glasses to view her computer screen comfortably at a distance of 55.0 cmcm . PART A What should be the power of the lenses for her glasses?

-2.5

A microscope has an objective lens with a focal length of 15.0 mmmm . A small object is placed 0.70 mmmm beyond the focal point of the objective lens. What is the magnification of the real image?

-21

Measurements on the cornea of a person's eye reveal that the magnitude of the front surface radius of curvature is 7.88 mmmm , while the magnitude of the rear surface radius of curvature is 7.20 mmmm (see (Figure 1)), and that the index of refraction of the cornea is 1.38. If the cornea were simply a thin lens in air, what would be its focal length?

-220mm

The eyepiece of a refracting astronomical telescope, shown below, has a focal length of 7.00 cmcm . The distance between objective and eyepiece is 1.70 mm , and the final image is at infinity. What is the angular magnification of the telescope?

-23.3

part c f the tooth has an actual length of 5.00 cmcm, how long does it appear to the observers?

-4.7

part G What is the image distance?

-6.67 cm

What are the path-length differences at Points A, C, and D (respectively, ΔdAΔdA, ΔdCΔdC, and ΔdDΔdD)? (Figure 3) Enter your answers numerically in terms of λλlambda separated by commas. For example, if the path-length differences at Points A, C, and D are 4λ4λ, λ/2λ/2, and λλ, respectively, enter 4,.5,1.

0,1.5,0.5

A laser with wavelength d/8d/8 is shining light on a double slit with slit separation 0.500 mmmm . This results in an interference pattern on a screen a distance LLL away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits What is the wavelength λ2λ2lambda_2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if ddd = 0.500 mmmm ?

0.109

Sound with frequency 1300 HzHz leaves a room through a doorway with a width of 1.02 mm . At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound? Use 344 m/sm/s for the speed of sound in air and assume that the source and listener are both far enough from the doorway for Fraunhofer diffraction to apply. You can ignore effects of reflections.

0.262radians convert degree to radians

PART C What is the distance Δymax−minΔymax−minDeltay_max-min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

0.400m

f he views the photograph from a distance of 2.35 mm , how tall is its image on his retina?

0.691

If a farsighted person has a near point that is 0.600 mm from the eye, what is the focal length f2f2f_2 of the contact lenses that the person would need to be able to read a book held at 0.350 mm from the person's eyes?

0.840

Why are the two-source interference equations not valid for an observer on a road far away from two neighboring radio towers for different radio stations? sources emit at different frequencies (i.e., not monochromatic sources) incoherent sources observed from a distance similar to or smaller than the separation between the sources

1 and 2 only

What are the path-length differences at Points L to P? (Figure 5) Enter your answers numerically in terms of λλlambda separated by commas. For example, if the path-length differences at Points L, M, N, O, and P are 5λ5λ, 2λ2λ, 32λ32λ, λλ, and 6λ6λ, respectively, enter 5,2,1.5,1,6

1,1,1,1,1

Part B Part complete At what distances from source A is there destructive interference between points A and B?

1,4m

Visible light passes through a diffraction grating that has 900 slits per centimeter, and the interference pattern is observed on a screen that is 2.40 mm from the grating In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.18 mmmm . What is the difference between these wavelengths?

1.47×10−8m

Your FM station has a frequency of 100 megahertz. The speed of light is about 3.00×1083.00×108 meters per second. What is the distance ddd between points A and B? Express your a

1.5

In one form of cataract surgery the person's natural lens, which has become cloudy, is replaced by an artificial lens. The refracting properties of the replacement lens can be chosen so that the person's eye focuses on distant objects. But there is no accommodation, and glasses or contact lenses are needed for close vision. What is the power, in diopters, of the corrective contact lenses that will enable a person who has had such surgery to focus on the page of a book at a distance of 23 cmcm ?

1/0.23= 4.3

If the lens has a focal length of 11.0 cmcm , and the image is to be at infinity, how high should the stand hold the lens above the stamp?

11 CM

What is the focal length of the lens?

14

shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 1.5 cmcm along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: part b What is the focal length of the lens?

14 cm

You have been asked to measure the width of a slit in a piece of paper. You mount the paper 80.080.0 centimeters from a screen and illuminate it from behind with laser light of wavelength 633633 nanometers (in air). You mark two of the intensity minima as shown in the figure, and measure the distance between them to be 17.917.9 millimeters What is the width aaa of the slit?

170 UM

Which is the telephoto focal length, 6.25mm or 19.2mm ?

19.2 mm

If the angle θθtheta in the two-source interference equations is small, then using small-angle approximations yields the equation ym=R(m+1/2)λdym=R(m+1/2)λd, where RRR is the distance from the sources to the points where they are being detected (in Young's experiment the screen, in this example the road), and ymymy_m is the distance from the central maximum to the minimum of order mmm. Use this equation to find the distance from the central maximum to the minimum in the previous part.

1900

Which of the following statements explain why the two-source interference equations are not valid for an observer far away from two red LED signal lights? not monochromatic sources incoherent sources observed from a distance similar to or smaller than the separation between the sources

2 only

A simple magnifier for viewing postage stamps and other pieces of paper consists of a thin lens mounted on a stand. When this device is placed on a stamp, the stand holds the lens at the proper distance from the stamp for viewing. (See (Figure 1).) If the lens has a focal length of 11.0 cmcm , and the image is to be at infinity, what is the angular magnification of the device ?

2.27

A 50-year-old optometry patient focuses on a 6.50 cmcm -tall photograph at his near point. (See the table.) We can model his eye as a sphere 2.50 cmcm in diameter, with a thin lens at the front and the retina at the rear.(Figure 1) What is the effective focal length of his eye when he focuses on the photo?

2.35

Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points along the line connecting the two sources. At what distance from source A is there constructive interference between points A and B?

2.5

If you have a thin film of thickness 300 nmnm, what is the third-longest wavelength λ3,constructiveλ3,constructivelambda_3,constructive of light that exhibits constructive interference with the reflected light? Note that this corresponds to m=3

200 nm

If an eyepiece with a focal length of 2.5 cmcm is used, with a final image at infinity, what will be the overall angular magnification of the object?

210

The image formed by a microscope objective with a focal length of 5.00 mmmm is 155 mmmm from its second focal point. The eyepiece has a focal length of 27.0 mm

296.2 mm fist add 155 +5 = 160 then convert to cm

Assume that light is incident normal to the surface of a film of thickness ddd. How much farther does the light reflected from the back surface travel than the light reflected from the front surface?

2d

For constructive interference to occur, the difference between the two paths must be an integer multiple of the wavelength of the light (as is true in any interference problem), i.e. the general criterion for constructive interference is mλm,constructive=2dm where mm is a positive integer. This is usually stated in the slightly more explicit form λm,constructive=2d/m Given the thickness of the film, d, what is the longest wavelength λλlambda that can exhibit constructive interference?

2d

part b The unaided eye can distinguish two points at its near point as separate if they are about 0.10 mmmm apart. What is the minimum separation that can be resolved with this microscope?

3.4 x 10 ^-4

A scientist notices that an oil slick floating on water when viewed from above has many different colors reflecting off the surface, making it look rainbow-like (an effect known as iridescence). She aims a spectrometer at a particular spot and measures the wavelength to be 750 nmnm (in air). The index of refraction of water is 1.33. The index of refraction of the oil is 1.20. What is the minimum thickness ttt of the oil slick at that spot?

313

A microscope has an objective lens with a focal length of 15.0 mmmm . A small object is placed 0.70 mmmm beyond the focal point of the objective lens. part A At what distance from the objective lens does a real image of the object form?

340 mm

A SLR digital camera often has pixels measuring 8.00 μmμm ×× 8.00 μmμm . How many such pixels does the height of this image cover? Express your answer in number of pixels to two sig

3900

How tall is the image of the photo on his retina? Is the image mentioned in part C erect or inverted? Real or virtual?

4.06 MM The image is inverted and real.

The criterion for destructive interference is very similar to the criterion for constructive interference. For destructive interference to occur, the difference between the two paths must be some integer number of wavelengths plus half a wavelength: (m+12)λm,destructive=2d(m+12)λm,destructive=2d, or λm,destructive=2dm+12 where m is a nonnegative integer. What is the second-longest wavelength λ1,destructiveλ1,destructivelambda_1,destructive that will not be visible (i.e., will have strong destructive interference for the reflected waves) when reflected from a film of thickness 300 nmnm? Note that the longest wavelength corresponds to m=0m=0 for destructive interference. This is why the notation used for the second-longest wavelength is λ1,destructiveλ1,destructivelambda_1,destructive instead of λ2,destructiveλ2,destructivelambda_2,destructive.

400 nm

Now assume that the oil had a thickness of 200 nmnm and an index of refraction of 1.5. A diver swimming underneath the oil slick is looking at the same spot as the scientist with the spectromenter. What is the longest wavelength λwaterλwaterlambda_water of the light in water that is transmitted most easily to the diver?

451

You want to take a full-length photo of your friend who is 1.80 mm tall, using a 35.0 mmmm camera having a 50.0 mmmm lens. The image dimensions of 35.0 mmmm film are 24.0 mmmm ×× 36.0 mmmm and you want to make this a vertical photo in which your friend's image completely fills the image area part b How far is the lens from the film?

5.10 cm

The focal length of a simple magnifier is 7.60 cmcm . Assume the magnifier to be a thin lens placed very close to the eye Part complete How far in front of the magnifier should an object be placed if the image is formed at the observer's near point, 25.0 cmcm in front of her eye?

5.83

The wavelength λλlambda that appears in the interference equations given in Parts B and D represents the wavelength of light within the medium of the film. So far we have assumed that the medium composing the film is air, but many thin-film problems will involve films with an index of refraction different from that of air. Suppose that the butterfly gets wet, thus filling the gaps between the keratin sheets with water (index of refraction n=1.33n=1.33). What wavelength λ0λ0lambda_0 in air will be strongly reflected now?

530 nm

A zoom lens is a lens that varies in focal length. The zoom lens on a certain digital camera varies in focal length from 6.25 mmmm to 19.2 mmmm . This camera is focused on an object 2.25 mm tall that is 1.35 mm from the camera Part A Part complete Find the distance s1s1 between the lens and the photo sensors and the height h1h1 of the image when the zoom is set to 6.25 mmmm focal length .

6.28,10.5

If the object is hhh = 1.50 mmmm high, what is the height of its image formed by the magnifier?

6.43

A certain digital camera having a lens with focal length 7.50 cmcm focuses on an object 1.90 mm tall that is 4.65 mm from the lens.

7.6

the focal length of the eyepiece of a certain microscope is 20.0 mm . The focal length of the objective is 8.50 mm . The distance between objective and eyepiece is 19.8 cm . The final image formed by the eyepiece is at infinity. Treat all lenses as thin. part A What is the distance from the objective to the object being viewed?

8.93

A thin film of polystyrene is used as an antireflective coating for fabulite (known as the substrate). The index of refraction of the polystyrene is 1.49, and the index of refraction of the fabulite is 2.409. What is the minimum thickness of film required? Assume that the wavelength of the light in air is 490 nanometers.

82.2

Now use the spherical mirror equation to find the image distance s′

90

If the glass has a refractive index of 1.55 and you use TiO2TiO2, which has an index of refraction of 2.62, as the coating, what is the minimum film thickness that will cancel light of wavelength 520 nmnm ?

99.2 m to nm

Consider a road that runs parallel to the line connecting a pair of radio towers that transmit the same station (assume that their transmissions are synchronized), which has an AM frequency of 10001000 kilohertz. If the road is 55 kilometers from the towers and the towers are separated by 400400 meters, find the angle θθtheta to the first point of minimum signal (m=0m=0). Hint: A frequency of 10001000 kilohertz corresponds to a wavelength of 300300 meters for radio waves.

=0.38radians

To further explore what this equation means, consider four sets of identical waves that move in the +x direction. A photo is taken of each wave at time ttt and is displayed in the figures below. Rank these sets of waves on the basis of the maximum amplitude of the wave that results from the interference of the two waves in each set.

A>B=D>C

Identify the fringe or fringes that result from the interference of two waves whose path difference differs by exactly 2λ

AD

Now consider a wave which is paired with seven other waves into seven pairs. The two waves in each pairing are identical, except that one of them is shifted relative to the other in the pair by the distance shown: −(1/2)λ−(1/2)λ 2λ2λ −5λ−5λ (3/2)λ(3/2)λ 00 (17/2)λ(17/2)λ (6/2)λ(6/2)λ Identify which of the seven pairs will interfere constructively and which will interfere destructively. Each letter represents a pair of waves.

BCEG,ADF

What is the power corresponding to the focal length found in part (C) in diopters?

D =1.56 diopters

What can one say about the image produced by a thin lens that produces a positive magnification?

It is virtual and erect.

Several thin films are stacked together in each butterfly wing scale. How would these multiple layers of thin films affect the light reflected by the butterfly's wings?

More 400-nmnm light would be reflected, because some of the light transmitted through the first layer could be reflected by the second layer, light transmitted by the second layer could be reflected by the third, etc.

Which of the following statements correctly describes rays 1 and 2 and their path difference?

Ray 1 undergoes a half-cycle phase shift. Ray 2 does not undergo any phase shift. The path difference between rays 1 and 2 is about 2T

Listed below are alterations made, one at a time, to the original experiment, and the experiment is repeated. After each alteration, the experiment is returned to its original configuration. Which of these alterations decreases the angles at which the diffraction minima appear?

The experiment is conducted in a water-filled tank. A green, rather than red, light source is used. The slit width is doubled. Submit

A certain digital camera having a lens with focal length 7.50 cmcm focuses on an object 1.90 mm tall that is 4.65 mm from the lens. Is the image on the photocells upright or inverted? Real or virtual?

The image is inverted and real.

What must result if the eyepiece lens of a refracting telescope is replaced with a lens that has a shorter focal length?

The length of the telescope must be reduced. The angular magnification produced by the telescope increases. The angular size of the image seen by the viewer increases. Submit

When glasses (or contact lenses) are used to correct nearsightedness, where should the corrective lens form an image of an object located at infinity in order for the eye to form a clear image of that object?

The lens should form the image at the far point.

part c When glasses (or contact lenses) are used to correct farsightedness, where should the corrective lens form an image of an object located between the eye and the near point in order for the eye to form a clear image of that object?

The lens should form the image at the near point.

A large aquarium has portholes of thin transparent plastic with a radius of curvature of 1.85 mm and their convex sides facing into the water. A shark hovers in front of a porthole, sizing up the dinner prospects outside the tank Does the shark appear to be right side up or upside down?

The shark appears to be right side up.

If the entire apparatus were submerged in water, would the width of the central peak change?

The width would decrease.

The same double-slit experiment is then immersed in water (with an index of refraction of 1.33) and repeated. When in the water, what happens to the interference fringes?

They are more closely spaced than in air by a factor of 1.33.

Which are the components of a typical refracting telescope?

a converging objective and a converging eyepiece

Now look at the waves emitted from two identical sources (e.g., two identical rocks that fall into a lake at the same time). The sources emit identical waves at the exact same time. (Figure 3) Identify whether the waves interfere constructively or destructively at each point A to D. For points A to D enter either c for constructive or d for destructive interference. For example if constructive interference occurs at points A, C and D, and destructive interference occurs at B, enter cdcc.

ccdd

Part A Part complete Using only the ray shown, decide what type of lens this is.

converging

Young's experiment is performed with light of wavelength 502 nmnm from excited helium atoms. Fringes are measured carefully on a screen 1.20 mm away from the double slit, and the center of the 20th fringe (not counting the central bright fringe) is found to be 10.4 mmmm from the center of the central bright fringe.

d =1.16mm

(Figure 1) shows an object and its image formed by a thin lens. What type of lens is it?

diverging

Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 41.0 cm from his eyes instead of the usual 25.0 cm . PART A Is this person nearsighted or farsighted?

farsighted

Joe now shifts his focus from the tree to the squirrel. To do this, the ciliary muscles in his eyes must have _____ the curvature of the lens, resulting in a(n) _______ focal length for the cornea-lens system. Note that curvature is different from radius of curvature.

increase and decrease

Two lasers are shining on a double slit, with slit separation ddd. Laser 1 has a wavelength of d/20d/20, whereas laser 2 has a wavelength of d/15d/15. The lasers produce separate interference patterns on a screen a distance 6.00 mm away from the slits Which laser has its first maximum closer to the central maximum? PART B What is the distance Δymax−maxΔymax−maxDeltay_max-max between the first maxima (on the same side of the central maximum) of the two patterns?

laser 1 PART B 0.1 M

Red light of wavelength 633 nmnm from a helium-neon laser passes through a slit 0.340 mmmm wide. The diffraction pattern is observed on a screen 2.75 mm away. Define the width of a bright fringe as the distance between the minima on either side. part A What is the width of the central bright fringe?

part A 0.0102

At Point A is the interference between the two sources constructive or destructive? part a At Point A is the interference between the two sources constructive or destructive? part b At Point B is the interference between the two sources constructive or destructive? Part C At Point C is the interference between the two sources constructive or destructive? Part D At Point D is the interference between the two sources constructive or destructive?

part A constructive part b destructive part c destructive part d constructive

A researcher measures the thickness of a layer of benzene (nn = 1.50) floating on water by shining monochromatic light onto the film and varying the wavelength of the light. She finds that light of wavelength 600 nmnm is reflected most strongly from the film. What does she calculate for the minimum thickness of the film?

t =100 nm m to nm

A thin film of polystyrene of refractive index 1.49 is used as a nonreflecting coating for Fabulite (strontium titanate) of refractive index 2.409. What is the minimum thickness of the film required? Assume that the wavelength of the light in air is 440 nmnm .

t=73.8nm

Which of the following are functions of the eyepiece lens of a refracting telescope?

to produce an image whose angular size is greater than that of the object to magnify the image produced by the objective lens

If the diameter of a lens is reduced, what happens to the magnification produced by the lens?

unchanged

Examining your image in a convex mirror whose radius of curvature is 24.2 cmcm , you stand with the tip of your nose 11.0 cmcm from the surface of the mirror. Where is the image of your nose located?

v= -5.75

How tall is the image on the sensor array?

|h′| =3.11cmcm

A beam of laser light of wavelength 632.8 nmnm falls on a thin slit 4.00×10−3 mmmm wide. After the light passes through the slit, at what angles relative to the original direction of the beam is it completely cancelled when viewed far from the slit?

|θ1|, |θ2|, |θ3| =9.10,18.4,28.3

How far from the central spot does the next pair of bright spots occur on the screen?

|θ3|=52.1

Due to interference with reflections off the water, certain wavelengths will be weak when they reach the balloon. What is the maximum wavelength λλlambda that will interfere destructively?

λ =2hx/ d

A diffraction grating has 5530 lines/cmlines/cm . When a beam of monochromatic light goes through it, the second pair of bright spots occurs at ±±26.0 cmcm from the central spot on a screen 42.0 cmcm past the grating. What is the wavelength of this light?

λ =476nm

What is the maximum wavelength λλlambda that will interfere constructively? Express your answer in terms of hhh, ddd, and xxx.

λ =4hx/d

Consider an object with s=12cms=12cm that produces an image with s′=15cms′=15cm. Note that whenever you are working with a physical object, the object distance will be positive (in multiple optics setups, you will encounter "objects" that are actually images, but that is not a possibility in this problem). A positive image distance means that the image is formed on the side of the lens from which the light emerges. part E Is the image real or virtual? Think about the magnification and how it relates to the sign of s′

virtual

Which of the following best decribes the object being viewed by the telescope?

The object is essentially infinitely far away.

Joe first focuses his attention (and his eyes) on the tree. The focal length of the cornea-lens system in his eye must be __________ the distance between the front and back of his eye.

less than

(Figure 1) shows an object and its image formed by a thin lens. What is the focal length of the lens?

4.8

Consider a concave mirror that has a focal length ff. In terms of ff, determine the object distances that will produce a magnification of -3

4/3

Part A - Practice Problem:Part complete An ice fisherman would like to check the thickness of the ice to see whether it is safe to walk on. He knows that the ice (nicenice = 1.309) should be 19 cmcm thick to be safe. If he looks straight down through the ice, how thick will the ice appear to be if it is just thick enough for safe walking?

- 14.5 cm

Consider an object with s=12cms=12cm that produces an image with s′=15cms′=15cm. Note that whenever you are working with a physical object, the object distance will be positive (in multiple optics setups, you will encounter "objects" that are actually images, but that is not a possibility in this problem). A positive image distance means that the image is formed on the side of the lens from which the light emerges. part C What is the magnification mmm of the lens? Part D Think about the sign of s′ and the sign of y′which you can find from the magnification equation, knowing that a physical object is always considered upright. Which of the following describes the nature and orientation of the image?

-1.25 real and inverted

Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 2.3 cm

-1.62

In this example we will apply the thin-lens equation to a lens that has two concave surfaces. The two surfaces of the lens shown (Figure 1) have radii of curvature with absolute values of 20 cmcm and 5.0 cmcm. The index of refraction is 1.52. What is the focal length ff of the lens? A double-concave lens with index of refraction n=1.46n=1.46 has two surfaces with radii of curvature with absolute values 12.0 cmcm and 10.0 cmcm . What is the focal length of the lens? Express your answer to three significant figures and include appropriate units.

-11.9

The left end of a long glass rod 15.0 cm in diameter has a convex hemispherical surface 7.50 cm in radius. The refractive index of the glass is 1.60. Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end: (a) infinitely far, (b) 30.0 cm , and (c) 5.00 cm . S c = 5

-13.3

part c Determine the position sbsbs_b of the image if an object is placed in air on the axis of the rod 1.00 cmcm from the left end of the rod.

-2 cm

part b If a nearsighted person has a far point dfdfd_f that is 3.50 mm from the eye, what is the focal length f1f1f_1 of the contact lenses that the person would need to see an object at infinity clearly?

-3.50

A large aquarium has portholes of thin transparent plastic with a radius of curvature of 1.85 mm and their convex sides facing into the water. A shark hovers in front of a porthole, sizing up the dinner prospects outside the tank. If one of the shark's teeth is exactly 47.0 cmcm from the plastic, how far from the plastic does it appear to be to observers outside the tank? (You can ignore refraction due to the plastic.)

-33.24

A convex spherical mirror has a radius of curvature of 11.0 cm Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 15.0 cm

-4.03

A convex spherical mirror has a radius of curvature of 11.0 cmcm . Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 15.0

-4.03

Your ear is 10.0 cmcm behind the tip of your nose; where is the image of your ear located?

-7.68

part F What is the object distance? You will need to use the magnification equation to find a relationship between s and s′. Then substitute into the thin lens equation to solve for s.

12 cm

part I What is the x coordinate of the object? Keep in mind that a real image and a real object should be on opposite sides of the lens. Express your answer in centimeters, as a fraction or to three significant figures. part J Is the lens converging or diverging? part K Find the focal length of the lens.

12 cm converging part k = 8 cm

The left end of a long glass rod, 6.00 cm in diameter, has a convex hemispherical surface 3.00 cm in radius. The refractive index of the glass is 1.60. Determine the position sbsbs_b of the image if an object is placed in air on the axis of the rod 13.0 cm to the left of the end of the rod

13 cm

An object is located 29.0 cmcm from a certain lens. The lens forms a real image that is twice as high as the object. What is the focal length of this lens?

19.3

Find the distance s2s2 between the lens and the photo sensors and the height h2h2 of the image when the zoom is set to 19.2 mmmm .

19.5mm. ,32.5 mm

part b Now replace the lens used in Part A with another lens. The new lens is a diverging lens whose focal points are at the same distance from the lens as the focal points of the first lens. If the object is 5.00 cmcm high, what is the height of the image formed by the new lens? The object is still located 29.0 cmcm from the lens.

2 cm

A convex spherical mirror has a radius of curvature of 11.0 cm Calculate the size of the image.

2.144

(Figure 1) shows an object and its image formed by a thin lens. What is the height of the image?

2.44

You want to take a full-length photo of your friend who is 1.80 mm tall, using a 35.0 mmmm camera having a 50.0 mmmm lens. The image dimensions of 35.0 mmmm film are 24.0 mmmm ×× 36.0 mmmm and you want to make this a vertical photo in which your friend's image completely fills the image area part A How far should your friend stand from the lens?

2.55 m

of the water in a swimming pool. A child standing on the diving board drops a ball into the pool directly above the swimmer. The swimmer sees the ball dropped from a height of 3.5 mm above the water. From what height was the ball actually dropped?

2.6

A convex spherical mirror has a radius of curvature of 11.0 cm Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 10.0 cm part b Calculate the size of the image.

2.84

A converging lens forms an image of an 7.50 mmmm -tall real object. The image is 11.5 cmcm to the left of the lens, 3.40 cmcm tall, and upright. What is the focal length of the lens?

3.26

A convex spherical mirror has a radius of curvature of 11.0 cm Calculate the location of the image formed by an 8.00-mm-tall object whose distance from the mirror is 10.0 cm

3.55

What is the focal length f of this mirror?

30

A concave mirror has a radius of curvature of 34.4 cm part A What is its focal length? part B A ladybug 7.75 mmmm tall is located 21.8 cm from this mirror along the principal axis. Find the location of the image of the insect.

34.4/2=17.2 part b 81.6

(Figure 1) shows an object and its image formed by a thin lens. Assume that L = 15.2 cm and y= 3.30 mm What is the height of the image?

4.60 mm

A converging lens with a focal length of 6.80 cm forms an image of a 3.60 mmmm -tall real object that is to the left of the lens. The image is 1.20 cm tall and erect. Where are the object and images located? Is the image real or virtual?

4.74, -15.78 virtual

part b Calculate the size of the image.

5.64

Consider an object with s=12cms=12cm that produces an image with s′=15cms′=15cm. Note that whenever you are working with a physical object, the object distance will be positive (in multiple optics setups, you will encounter "objects" that are actually images, but that is not a possibility in this problem). A positive image distance means that the image is formed on the side of the lens from which the light emerges. part A Find the focal length of the lens that produces the image described in the problem introduction using the thin lens equation. part B Considering the sign of f , is the lens converging or diverging?

6.67 converging

The microscope available in your biology lab has a converging lens (the eyepiece) with a focal length of 2.50 cmcm mounted on one end of a tube of adjustable length. At the other end is another converging lens (the objective) that has a focal length of 1.00 cmcm . When you place the sample to be examined at a distance of 1.30 cmcm from the objective, at what length lll will you need to adjust the tube of the microscope in order to view the sample in focus with a completely relaxed eye?

6.83

Part B (Figure 1) shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 1.5 cmcm along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: Using only the ray shown, decide what type of lens this is. What is the focal length of the lens?

converging

shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 1.5 cmcm along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: Using only the ray shown, decide what type of lens this is.

converging

Finally, Joe turns his attention to the mountain in the distance but finds that he cannot bring the mountain into focus. This is because he is nearsighted. But when Joe puts on his glasses, he can see the mountain clearly. To adjust for his nearsightedness, his glasses must contain _____ lenses.

diverging

A lens produces a real image of a real object. part A Is the image inverted or upright? inverted part B Is the lens diverging or converging? The image produced by the lens is real. Diverging lens produces only virtual image. The converging lens produces real image. Thus, the lens is converging. part c Is the image enlarged or reduced in size? The lens produced a real image of real object. The converging lens can produce a real image of any size that is enlarged, same or diminished according to the position of the real object. The position of the object with respect to lens is not given so the size of the image cannot be determined.

part A inverted part B converging part C the image size cannot be determined

The near point (the smallest distance at which an object can be seen clearly) and the far point (the largest distance at which an object can be seen clearly) are measured for six different people. part A Which, if any, of these people require bifocals to correct their vision? part B Which, if any, of these people require bifocals to correct their vision? part C Which, if any, of these people's vision can be corrected using only converging lenses?

part a BCE part b BE part C AF

The left end of a long glass rod 15.0 cmcm in diameter has a convex hemispherical surface 7.50 cmcm in radius. The refractive index of the glass is 1.60. Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end: (a) infinitely far, (b) 30.0 cmcm , and (c) 5.00 cmcm . part a infinitive

part a 20 cm

The left end of a long glass rod 15.0 cm in diameter has a convex hemispherical surface 7.50 cm in radius. The refractive index of the glass is 1.60. Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end: (a) infinitely far, (b) 30.0 cm , and (c) 5.00 cm . part b s'b= 30

part b 34.3

Consider a concave mirror that has a focal length ff. In terms of ff, determine the object distances that will produce a magnification of part b -4

part b 1+ 1/4= 5/4=1.25

Consider a concave mirror that has a focal length ff. In terms of ff, determine the object distances that will produce a magnification of part c -5

part c 1+1/5= 1.2

Look at the signs of your answers to determine which of the following describes the image formed by this mirror:

real and inverted

What is the value of s′ obtained from this new equation?

s = -s

When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.50 cmcm -tall object is 53.0 cmcm to the left of a converging lens of focal length 40.0 cmcm . A second converging lens, this one having a focal length of 60.0 cmcm , is located 300 cmcm to the right of the first lens along the same optic axis Part B Part complete I 1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

s'1, /y1/ = 107,3.60cm

When two lenses are used in combination, the first one forms an image that then serves as the object for the second lens. The magnification of the combination is the ratio of the height of the final image to the height of the object. A 1.50 cmcm -tall object is 53.0 cmcm to the left of a converging lens of focal length 40.0 cmcm . A second converging lens, this one having a focal length of 60.0 cmcm , is located 300 cmcm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1I1) formed by the lens with a focal length of 40.0 cm

s'1, /y1/ = 163,4.62cm

To form the virtual and enlarged images seen by the observer, the telescope should be designed so that the image formed by the objective falls where?

slightly inside the focal length of the eyepiece