Chapter 13 Light and Geometric Optics

what is Snell's law of refraction?

(n1)sin(theta1) = (n2)sin(theta2)

What is the index of refraction of a vacuum

1

Focal length is equal to

1/2r

All electromagnetic waves, regardless of frequency, travel through a vacuum at what speed?

3 x 10^8 m/s

speed of light in a vacuum

3.00 x 10^8 m/s

Violet has a wavelength of

400 nm

What is Planck's constant?

6.626 x 10^-34 Js

Red light has a wavelength of

750 nm

What is a concave mirror?

A mirror that curves inward

What is a curved mirror?

A mirror with a curved reflective surface

The light emitted by a liquid crystal display (LCD), like the screens on cell phones and laptops, is plane polarized. Suppose the unpolarized backlight of the screen has an intensity of I0. If the light coming from the screen is polarized on a vertical axis, what intensity will pass through a horizontally oriented polarizing filter? A. 0 W B. I0/4 C. I0/2 D. I0

A; If we have a vertically polarized beam of light that is passing through a filter that is designed only to allow horizontal components of oscillation through, there is no horizontal component of the vertical oscillation, so nothing comes through.

A ray of light traveling through Medium #1 (n1 = 1) strikes the boundary with Medium #2 (n2 = 2). If the angle that the reflected ray makes with the boundary is 30°, then what is the angle of refraction? A. 26° B. 33° C. 52° D. 72°

A; The Law of Reflection states that the angle of reflection is equal to the angle of incidence. The angle of reflection, measured from the normal, is 90° − 30° = 60°, therefore the angle of incidence is also 60°. Snell's Law states that n1sin θ1 = n2sin θ2, where θ1 and θ2 are, respectively, the angles of incidence and refraction (also measured from the normal). Since n1 < n2, θ1 > θ2. This eliminates choice D. Substituting values, we see that (1)sin 60° sqrt 3/2= (2)sin θ2. sin 60° = , which is approximately 0.85, so sin θ2 is approximately 0.85 / 2 = 0.43. The exact angle is inaccessible without a calculator, but because sin 30° = 0.5, θ2 must be some value between 0° and 30°. Choice A is the only possibility in that range.

When red light (λ = 700 nm in a vacuum) passes into a medium with an index of refraction of n = 1.4, its new wavelength is equal to which of the following? A. 500 nm B. 700 nm C. 928 nm D. Cannot be determined without knowing the index of refraction of the incident medium

A; The speed of light, v, in a medium with index of refraction n, is given by v= c / n, where c is the speed of light in a vacuum (i.e. 3 × 108 m/s). For all waves, v = fλ, where f is the frequency and λ is the wavelength. When a wave passes into a new medium, its frequency stays the same, so we can say that, in a vacuum, c = fλvacuum and, in the medium, (c / n) = fλmedium. Dividing the first equation by the second yields n = λvacuum / λmedium, which means that λmedium = λvacuum / n = (700 nm) / 1.4 = 500 nm.

A single photoelectron ejected from a metal target will have a greater chance of reaching the detector plate if: A. it is ejected by a dim ultraviolet light and the detector voltage is higher than the target voltage. B. it is ejected by a dim ultraviolet light and the detector voltage is lower than the target voltage. C. it is ejected by a bright infrared light and the detector voltage is higher than the target voltage. D. it is ejected by a bright infrared light and the detector voltage is lower than the target voltage.

A; This is a classic two-by-two question, where the two degrees of freedom are the nature of the light ejecting the photoelectron and the voltage between the plates. A higher initial kinetic energy will make reaching the detector plate more likely. Note that the initial kinetic energy of an ejected photoelectron depends upon the energy of the ejecting photon, hf, which is a function of frequency and not brightness (which would determine the number of photons). Since ultraviolet light has a higher frequency than infrared light, the ultraviolet light will correspond to higher KE photoelectrons that are more likely to strike the detector (eliminating choices C and D). The other factor that will increase the likelihood of striking the detector plate is if photoelectrons are attracted to it rather than repelled. By ΔPE = qV, a decreasing potential energy (indicating attraction) corresponds to a positive voltage for a negative charge like a photoelectron. Thus a higher detector voltage will attract electrons (eliminating choice B).

What is circular polarized light?

All of the light rays have electric fields with equal intensity but constantly rotating direction

All of the following are true about radio waves EXCEPT: A. they are electromagnetic. B. they are longitudinal. C. they have longer wavelengths than visible light. D. they do not require a medium.

B;

Both sound and light can experience: I. Refraction II. Diffraction III. Polarization A. I only B. I and II only C. II and III only D. I, II and III

B;

Assume that the ray of sunlight strikes the water, making an angle of 60 degrees with the surface. What is the angle of reflection? A. 15 degrees B. 30 degrees C. 60 degrees D. 90 degrees

B; Be careful. If the incident ray makes an angle of 60 with the surface, then it makes an angle of 30 degrees with the normal. Therefore, the angle of incidence is 30 degrees.

A light source emits photons that hit a photodetector. All of the following would increase the TOTAL energy hitting the photodetector EXCEPT: A. increasing the area of the photodetector. B. increasing the wavelength of light being used. C. increasing the number of photons emitted per second. D. increasing the time that the photodetector collects photons.

B; If more photons (with the same energy) hit the photodetector, then more total energy will be detected. Increasing the area, the time and rate at which photons are created would all do this. Choices A, C and D can be eliminated. The energy of each photon is given by E = hf, where h is Planck's constant and f is the frequency of light. The relationship between wavelength, λ, and frequency is given by c = fλ, where c is the speed of light. Increasing the wavelength would decrease the frequency which would then decrease the energy of the photons. This would therefore decrease the total energy hitting the photodetector.

The index of refraction of water is about 4/3. Suppose you aimed a laser and a sonar gun (emitting a semi-coherent beam of sound waves) from the edge of a lake down toward the water, each with an angle of incidence of 45 degrees. Which of the following would most likely occur? A. Both the light ray and sound beam would partly transmit into the water and would bend toward the normal. B. The light ray would partly transmit into the water and would bend toward the normal; The sound beam might partly transmit, but if so would bend away from the normal C. Both the light and the sound would partly transmit and both would bend away from the normal D. Neither light nor sound would enter the water.

B; Light will slow down. Bends toward normal. Sound speed up in liquids than in gases, opposite of what light is doing. Bends away from normal.

What is refraction?

Bending of light

What is x-ray diffraction?

Bombarding DNA with x-rays to produce a picture

When light passes through a certain medium that is surrounded by air, the critical angle for total internal reflection is 45°. If that medium is submerged in water (n = 1.33), what is the new critical angle? A. 20° B. 34° C. 70° D. There is no critical angle

C; For total internal reflection to occur, light must be incident in the medium with the larger index of refraction. If the Angle of Incidence (measured with the normal) is equal to the critical angle, then the angle of refraction is 90°. Snell's Law dictates that n1sin θc = n2sin 90°, where θc is the critical angle. Therefore θc = sin−1(n2 / n1). Increasing n2 would cause θ2 to increase, provided that n2 does not exceed n1. This eliminates choices A and B. Deciding between choices C and D requires determining whether n1 is greater than 1.33: if it is, then there will be a critical angle (because the inverse sine will be defined for a fraction less than one), eliminating D. Applying Snell's Law for n2 equal to 1 yields: 1.4 Since this is greater than 1.33, there will still be a critical angle when the medium is surrounded by water. Choice D can be eliminated.

A ray of light traveling through Medium #1 strikes the boundary with Medium #2 at an angle of 35° from the normal. If the angle between the reflected and refracted rays is 95°, then what is the angle of refraction? A. 30° B. 40° C. 50° D. 55°

C; The Law of Reflection states that the angle of reflection equals the angle of incidence, therefore the reflected ray must also make a 35° angle with the normal. This means that the angle that the reflected ray makes with the boundary is 90° − 35° = 55°. Since the angle between the reflected and refracted rays is 95°, the refracted ray must make a 95° − 55° = 40° angle with the boundary. The angle of refraction is the angle that the refracted ray makes with the normal, which is therefore 90° − 40° = 50°.

ray of light traveling through Medium #1 (index of refraction = n1) strikes the boundary with air at angle of 30° from the boundary. If total internal reflection occurs, then what is necessarily true about n1? A. n1 < sqrt 3/2 B. n1 < 2 / sqrt 3 C. n1 > 2 / sqrt 3 D. n1 > 2

C; The index of refraction, n, of a medium is defined as c / v, where c is the speed of light in a vacuum and v is the speed of light in the medium. Since nothing can travel faster than c, the index of refraction for any medium will always be ≥ 1. This eliminates choice A. If the angle that the incident ray makes with the boundary is 30°, then the angle of incidence (measured from the normal) is 90° − 30° = 60°. When the angle of incidence is greater than the critical angle, total internal reflection occurs. This means that the critical angle must be smaller than 60°. If the angle of incidence is equal to the critical angle, then the refracted ray will be equal to 90°. Using Snell's Law yields n1sin θc = n2sin 90°. Since n2 = 1 (air) and sin 90° = 1, this means that n1 = 1 / sin θc. If the critical angle is < 60°, then sin θc < sqrt 3 /2, which means that n1 > 2/ sqrt 3.

A ray of green light is passed through glass and hits the boundary that the glass makes with the air at the critical angle. All of the following changes would cause total internal reflection to occur EXCEPT: A. increasing the angle of incidence. B. using blue light instead of green light. C. using red light instead of green light. D. using glass with a higher index of refraction.

C; When light is incident in a medium, n1, at the critical angle, θc, then the angle of refraction in the surrounding medium, n2, is 90°. According to Snell's Law, n1sin θc = n2sin 90°. Since n2 = 1 (air) and sin90° = 1, this means that θc= sin−1(1 / n1). When light is incident at an angle greater than θc, the light will experience total internal reflection. From this, choice A, can be eliminated. If n1 is increased, then the critical angle will decrease. Assuming the angle of incidence remains the same, it will now be larger than the critical angle, causing total internal reflection. This eliminates choice D. Due to dispersion, blue light travels slower in glass than green light. This means that n1 for blue light is greater than n1 for red light. Using blue light would therefore decrease the critical angle and also cause total internal reflection, so choice B can be eliminated. Red light travels faster in glass than green light, decreasing the value of n1, which increases the critical angle. Now the angle of incidence will be less than θc, so total internal reflection will not occur.

Which of the following is true about red light? A. Its speed in a vacuum is greater than that of blue light. B. It has a shorter wavelength than blue light. C. It requires a medium. D. It is a transverse wave.

D;

Which of the following is true concerning the differences between sound waves and light? A. Both can travel through a vacuum B. Both can be polarized C. Both travel faster through water than through air D. Both can experience reflection, refraction and diffraction

D;

Which of the following statements is true regarding red photons and blue photons traveling through vacuum? A. Red light travels faster than blue light and carries more energy B. Blue light travels faster than red light and carries more energy C. Red light travels at the same speed as blue light and carries more energy D. Blue light travels at the same speed as red light and carries more energy

D;

A ray of light traveling through Medium #1 (n1 = 1) strikes the boundary with Medium #2 (n2 = 1.1). If the angle that the reflected ray makes with the boundary is 30°, then what is the angle of incidence? A. 27° B. 30° C. 52° D. 60°

D; The Angle of Incidence is defined as the angle that the incident ray makes with the normal (i.e. a line perpendicular to the boundary). Similarly, the Angle of Reflection is the angle that the reflected ray makes with the normal. Since the reflected ray makes a 30° angle with the boundary, the Angle of Reflection is 90° − 30° = 60°. The Law of Reflection states that the Angle of Reflection equals the Angle of Incidence. Therefore, the Angle of Incidence must also be 60°. Note that the indices of refraction do not matter.

A ray of light traveling in Medium #1 (n1 = 1.4) strikes the boundary with Medium #2 at an angle of 60° from the normal. If the angle between the reflected and refracted rays is 75°, then what is the index of refraction of Medium #2? A. 0.7 B. 1 C. 1.3 D. 1.7

D; The index of refraction, n, of a medium is defined as c / v, where c is the speed of light in a vacuum and v is the speed of light in the medium. Since nothing can travel faster than c, the index of refraction for any medium will always be ≥ 1. This eliminates choice A. According to the Law of Reflection, since the angle that the incident ray makes with the normal is 60°(i.e. the angle of incidence), the angle that the reflected ray makes with the normal will also be 60°. The angle that the reflected ray makes with the boundary should therefore be 90° − 60° = 30°. Since the angle between the reflected and refracted rays is 75°, the angled that the refracted ray makes with the boundary is 75° − 30° = 45°. This means that the angle that the refracted ray makes with the normal (i.e. the angle of refraction) is 90° − 45° = 45°. Snell's Law states that n1sin θ1 = n2sin θ2, where θ1 and θ2 are, respectively, the angles of incidence and refraction. Substituting values yields (1.4)sin(60°) = n2sin(45°),

When light passes from Medium #1 (index of refraction n1) to Medium #2 (index of refraction n2), the wavelength becomes smaller. Which of the following is true? A. The frequency in Medium #1 is greater than the frequency in Medium #2 B. The frequency in Medium #1 is less than the frequency in Medium #2 C. n1 > n2 D. n1 < n2

D; When a wave passes into a new medium, its frequency stays the same. This eliminates choices A and B. For waves, v = fλ, where v is the speed, f is the frequency and λ is the wavelength. If λ decreases when entering Medium #2, then v should also decrease. The relationship between v and n is given by n = c / v, where c is the speed of light in a vacuum. Therefore, since v1 > v2, this means than n1 < n2.

One light source emits bright red light while another source emits dim blue light. According to the photon theory of light: A. each red photon must have more energy than each blue photon. B. the red photons must be traveling slower than the blue photons. C. the red photons must be experiencing less diffraction than the blue photons. D. there must be more red photons being emitted per second than blue photons.

D; Whether light is thought of as a wave or as photons, all frequencies travel at 3 × 108 m/s in a vacuum and close to that speed in air. This eliminates choice B. (Note that even if the dispersion of light were considered, red light would travel faster than blue light). The energy of a photon is given by E = hf, where h is Planck's constant and f is the frequency of the light. Since the frequency of blue light is greater than that of red, the energy of blue photons is greater than the energy of red photons. This eliminates choice A. There is nothing in the question relating to diffraction, so we can eliminate choice C. (Note that even if diffraction were taken into account, red light diffracts more than blue light when passing through a small opening). The answer is D. Brightness corresponds to intensity, which is total energy per time per area. For red light to have higher intensity than blue light, there must be more red photons being emitted per second.

How does double slit diffraction and interference differ from single slit diffraction?

Double slit: creates fringes because light waves construct/deconstruct Single slit: Forms image of wide band of light (arc)

Energy of a photon equation

E = hf = hc/lambda

What is unpolarized light?

It is light that has no specific orientation of oscillation

What is the wave-particle duality of light?

Light is an electromagnetic wave. It can also be observed as a particle/photon.

What happens when the angle of incidence is equal to the critical angle?

Light refracts 90 degrees from the normal

Can sound waves be polarized?

No

Does sound travel through a vacuum?

No

How does the application of a polarized light filter impact the wavelength of light passing through the filter?

Plane polarization has no effect on the wavelength of light. Polarization does affect the amount of light passing through a medium and light intensity.

Contrast plane polarized light and circularly polarized light

Plane-polarized: Plane polarized light contains light waves with parallel electric field vectors. Circularly polarized: Circularly polarized light selects for a given amplitude and has a continuously rotating electric field.

Critical angle equation

Sin c = n2/n1

What is the critical angle?

The angle of incidence when the angle of refraction is 90 degrees

What is the center of curvature?

The center of curvature is the point at the center of the sphere

What is the focal length?

The distance from the lens to the principal focus

What is chromatic aberration?

The effect when many colors are seen toward the edge of the microscope field of vision (like a prisim)

What is dispersion of light?

The separation of visible light into its different colors

What is diffraction?

The spreading out of waves after passing through a slit/around an obstacle.

What is total internal reflection?

Total internal reflection is where all the light is reflected inside a material.

What happens when the angle of incidence is greater than the critical angle?

Total internal reflection occurs

True or false: Maxima in diffraction patterns are always equidistant between two minima

True

How do you transform unpolarized light into polarized light?

Using polarizing filters

What is a single slit system?

When light passes through a narrow opening, the light seems to spread out As the slit is narrowed, the light spreads out more.

Can light travel through a vacuum?

Yes, it does not require a medium

What is a plane mirror?

a mirror with a flat surface

What is a black body?

a perfect emitter and absorber of radiation

location of the dark fringes in a slit-lens system equation

a sin theta = ny

What mediums can light travel through?

all mediums

What is the law of reflection?

angle of incidence = angle of reflection

If the transmitting medium has a lower index of refraction than the incident medium then the ray will tend to bend ________ from the normal

away

n1 --> n1 = 1.33, n2 = 1 What way will the light ray bend?

away from the normal

If you put an object in front of a plane mirror, the image will appear ________ the mirror

behind

Concave mirrors are _______

converging

What is the radius of curvature?

distance from mirror to center of curvature

Convex mirrors are

diverging

What is polarized light?

electric field only ossicilates in one direction

An oscillating electric charge generates an _______ wave, which is composed off oscillating electric and magnetic fields

electromagnetic

The image will appear at the _____ _____ for all curved mirrors

focal point

When light parallel to the central axis of a concave mirror strikes a surface, its reflected through a point called the

focal point

When light parallel to the central axis of a convex mirror strikes the surface, it's reflected directly from the imaginary _______ ________ behind the mirror

focal point

Bright fringes are ____ between dark fringes

halfway

When waves interact with each other, the displacements of the waves add together in a process called

interference

An image is said to be real if

light actually converges at position of image

What is plane polarized light?

light confined to a single plane of vibration; light has their electric field components vibrating in a single plane

An image is said to be virtual if

light only appears to be coming from the position of the image but does not actually converge there

Light travels through water at an approximate speed of 2.25 x 10^8 m/s. What is the refractive index of water? A. .75 B. 1.33 C. 1.50 D. 2.25

n = c/v n = 3 x 10^8 m/s / 2.25 x 10^8 n = 1.33

You're standing on the shore of a lake and looking into the water (n water = 1.33). A little ways from shores you notice a minor swimming by. How far (horizontally) is the minnow from you compared to where you seem to be? A. Closer than it seems B. Exactly the same distance as it seems C. Farther than it seems D. It cannot be determined from the information given

n1 = water n2 = air light bends away from the normal, the fish appears closer than it seems

There can only be a critical angle for total internal reflection only if what?

n1 is greater than n2

Index of refraction equation

n=c/v

Reflected rays are measured with respect to the

normal

The ray diagram from a convex mirror shows two incident rays reflecting off the mirror. One ray is _______ to the axis and the other hits the ______ of the mirror, and is reflected at the same angle below the axis

parallel center

The ray diagram from a concave mirror shows two incident rays reflecting off the mirror. One ray is _______ to the axis and the other ray is ________ parallel to the axis

parallel reflected

What are photons?

particles of light

Normally, light waves oscillate equally in all directions _________ to the direction of propagation

perpendicular

The electric and magnetic field oscillate in phase with each other, ____________ to each other and to the direction of propagation

perpendicular

When unpolarized light strikes a filter, the portion of the waves vibrating in that direction pass through a portion of the wave vibrating _________ to the axis absorbed

perpendicular

An object that appears red is one that absorbs all colors except ________

red

In dispersion, _______ light deviates the least

red

A beam of light is incident on the boundary between air and a piece of glass whose index of refraction is sqrt 2. When would total internal reflection of this beam occur?

sin c = n2/n1 sin c = 1/ sqrt 2 sin c = sqrt 2/2 sin c = 45

When light travels through a material (not a vacuum), different frequencies will travel at different __________. This is a violation of big rule 1 for waves

speeds

What is the angle of refraction?

the angle between the refracted ray and the normal

What is the focal point?

the point at which the light rays meet

If the transmitting medium has a higher index of refraction than the incident medium, then the ray will bend ________ the normal

toward

n1 --> 2 n1 = 1, n2 = 1.33 What way will the light ray bend

toward the normal

Light is a ______ wave

transverse

only ___ waves can be polarized

transverse

The image in a plane mirror will always appear

upright (never inverted)

In dispersion, ________ deviates the most

violet

light that contains all the colors in equal intensity is perceived as

white