22 Reflection & Refraction of Light
What photon has the highest energy?
Ultraviolet
When light from the air hits a smooth piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass:
Will NOT change its frequency
A laser beam is incident at an angle of 28.2° to the vertical onto a solution of corn syrup in water. (a) If the beam is refracted to 19.22° to the vertical, what is the index of refraction of the syrup solution? (b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution. (c) Find its frequency in the solution. (d) Find its speed in the solution.
a) 1.44 n2=n1sinθ/sinθ2 n2= ((1)(sin28.2))/(sin19.22) b) 439 nm λm=λ/h λm= (632.8 nm)/1.44 c) 4.74x10^14 Hz f=c/λ f= (3.0x10^8 m/s)/ ((632.8 nm (10^-9)) d) 2.08x10^8 m/s v=c/h v= (3.0x10^8 m/s)/1.44
Find the energy of the following. Express your answers in units of electron volts, noting that 1 eV = 1.60 10-19 J. (a) a photon having a frequency of 6.80 1017 Hz (b) a photon having a wavelength of 2.00 102 nm
a) 2820 eV E=hf E=(6.63x10^-34Js)(6.8x10^17Hz) =(4.5x10^-16)(1eV/1.6x10^-19J) =(2.82x10^3eV)= 2820 eV b) 6.22 eV E=hc/λ E=((6.63x10^-34Js)(3.0x10^8 m/s))/((2.0x10^2nm)(10^-9)) =(9.95x10^-19J)(1eV/1.6x10^-19J) =6.22 eV
The speed of light in a vacuum is 3.00 x 108 m/s. Determine the speed of light through the following materials. air (n=1.00) ethanol (n=1.36) crown glass (n=1.52) zircon (n=1.91) diamond (n=2.42)
a. (3.00 x108 m/s)/1.00 = 3 x 108 m/s b. (3.00 x108 m/s)/1.36 = 2.21 x 108 m/s c. (3.00 x108 m/s)/1.52 = 1.97 x 108 m/s d. (3.00 x108 m/s)/1.91 = 1.57 x 108 m/s e. (3.00 x108 m/s)/2.42 = 1.24 x 108 m/s
Determine the critical angle for the following boundaries: air - crown glass (n=1.52) air - diamond (n=2.42) crown glass (n=1.52) - diamond (n=2.42) air - Lucite (n=1.40) air and a material through which light travels at a speed of 2.10 x 108 m/s
a. Critical angle = invsin(1.00/1.52) = 41.1 degrees. b. Critical angle = invsin(1.00/2.42) = 24.4 degrees. c. Critical angle = invsin(1.52/2.42) = 38.9 degrees. d. Critical angle = invsin(1.00/1.40) = 45.6 degrees. e. First find the index of refraction using n = (3.00 x 108 m/s) / (2.10 x108 m/s) = 1.42; then use the equation Critical angle = invsin(1.00/1.42) = 44.4 degrees.
If total internal reflection occurs at a glass-air surface, then _____.
no light is refracted
Which of the following describes what will happen to a light ray incident on an air-to-glass boundary at an angle of incidence less than the critical angle?
partial reflection, partial transmission At a boundary between any two materials, there will be both reflection and transmission. The only exception is when the light is incident in the more dense material and at an incident angle greater than the critical angle.
Which of the following describes what will happen to a light ray incident on an air-to-glass boundary?
partial reflection, partial transmission Upon reaching a boundary, a wave undergoes both reflection and transmission. The only exception is for light in the more dense medium and at angles of incidence greater than the critical angle; in such a case, total internal reflection occurs.
When light from air hits a smooth piece of glass (n = 1.5) with the ray perpendicular to the glass surface, which of the following will occur?
reflection and transmission at an angle of 0 degrees A portion of the light is reflected and a portion of the light is transmitted into the new medium. Since the angle of incidence is 0 degrees, there is no bending of the ray. Noticeable dispersion only occurs when there is refraction of light at two consecutive boundaries which are nonparallel.
A light ray in air enters and passes through a block of glass. What can be stated with regard to its speed after it emerges from the block?
speed is same as that before it entered glass
Which of the following describes what will happen to a light ray incident on an glass-to-air boundary at an angle of incidence greater than the critical angle?
total reflection At a boundary between any two materials, there will be both reflection and transmission. The only exception is when the light is incident in the more dense material and at an incident angle greater than the critical angle. Since the light in this problem is in the more dense medium (glass) and at an angle greater than the critical angle, total internal reflection will occur. No transmission will occur at this boundary for such angles.
A ray of white light, incident upon a glass prism, is dispersed into its various color components. Which one of the following colors experiences the greatest amount of refraction?
violet The shorter wavelengths of light undergo the most refraction. Thus, violet is refracted the most and red light is refracted the least. The fact that the various component colors of white light refract different amounts leads to the phenomenon of dispersion.
When the reflection of an object is seen in a plane mirror, the image is
virtual and upright
When light from air hits a smooth piece of glass with the ray perpendicular to the glass surface, the part of the light passing into the glass _____.
will not change its direction
The index of refraction for red light in water is 1.331 and that for blue light is 1.340. If a ray of white light enters the water at an angle of incidence of 57.75°, what are the underwater angles of refraction for the blue and red components of the light? (Enter your answers to at least two decimal places.) a) blue component b) red component
(a) 47.79° θblue= invsin(nair(sin θ1)/nblue) θblue= invsin(1.00)sin83°/1.340) (b) 48.22° θred= invsin(nair(sin θ1)/nblue) θred=invsin(1.000)sin83°/1.331)
A small underwater pool light is 1 m below the surface of a swimming pool. What is the radius of the circle of light on the surface, from which light emerges from the water? (nwater = 1.333).
1.14 m r= tanθc r=tan(invsin(n2/n1)) r=tan(invsin(1/1.33))
If the critical angle for internal reflection inside a certain transparent material is found to be 48.0 degrees, what is the index of refraction of the material? (Air is outside the material).
1.35 nr (sin(48)) = 1.00(sine (90)) nr = 1.00/sin(48) = 1.35
A light ray in air is incident on an air to glass boundary at an angle of 45.0 degrees and is refracted in the glass of 30.0 degrees with the normal. What is the index of refraction of the glass?
1.41 1.00 (sin(45)) = nr(sin(30)) 1.00(sin(45)/sin(30) = nr nr = 1.41
How much energy (in eV) does a photon of red light (λ=700 nm) have? (h=6.63x10^-34Js, c= 3.00x10^6 m/s, 1eV= 1.60x10^-19 J, 1nm= 10^-9)
1.78 eV
What value of inductance should be used in a series circuit with a capacitor of 1.8x10^-3 uF when designed to radiate a wavelength of 35 m?
1.9 x 10^-7 H 1.9 x 10^-4 mH f= c/λ f= (3x10^8 m/s)/35 =8.57x10^6 L= 1/(4(pi)^2f^2c) L= 1/(4(pi)^2(8.57x10^6)^2(1.8x10^-9)0
A ray of light is incident on the surface of a block of clear ice at an angle of 33.0° with the normal. Part of the light is reflected and part is refracted. Find the angle between the reflected and refracted light.
122.4° θ2=invsin((n1/n2)sinθ1) θ2=invsin((1/1.309)sin33)= 24.6° a=180°-(θ1+θ2) a=180°-(33+24.6) =122.4
Waves from a radio station with a wavelength of 600 m arrive at a home receiver distance 50 km away from the transmitter by two paths. One is direct-line path and the second by reflection from a mountain directly behind the receiver. What is the minimum distance between the mountain and receiver such that destructive interference occurs at the location of the listener?
150 m 2d=600/2
A ray of light strikes a thick sheet of glass (n = 1.5) at an angle of 25° with the normal. Find the angle of the ray REFRACTED off the glass surface with respect to the normal.
16 ° θ2 = invsin((n1/n2)(sinθ)) invsin(sin25/1.5)= 16 degrees
A ray of light in air is incident on an air-to-glass boundary at an angle of 30. degrees with the normal. If the index of refraction of the glass is 1.65, what is the angle of the refracted ray within the glass with respect to the normal?
18 degrees sinθr = 1.00 (sin(30)) / 1.65 = 0.3030 θr = inversesin(0.3030) = 17.6 degrees
As the angle of incidence is increased for a ray incident on a reflecting surface, the angle between the incident and reflected rays ultimately approaches what value?
180 ° The angle of incidence is the angle between the incident ray and the normal. As this angle approaches 90 degrees, the reflected ray also approaches a 90 degree angle with the normal; thus, the angle between the incident and reflected ray approach 180 degrees.
Light with a wavelength of 589 nm in a vacuum strikes the surface of an unknown liquid at an angle of 31.2° with respect to the normal of the surface. If the light travels at a speed of 1.97x10^8 m/s through the liquid, what is the angle of refraction?
19.9 ° sinθLiq= sin31.2/1.52 =0.341 θLiq= invsin(0.341)
If carbon tetrachloride has an index of refraction of 1.461, what is the speed of light through this liquid? (c = 3 x 108 m/s)
2.05 x 108 m/s V=c/n V= (3x108 m/s)/1.461
Water has an index of refraction of 1.333. What is the speed of light through it?
2.25x10^8 m/s v=c/n v=(3.0x10^8 m/s)/1.333
Determine the largest value of the angle a so that the ray is totally reflected at the face ac if the prism is immersed in a liquid with refractive index 1.12.
21° n1= 1.12 n2= 1.20 (prism) Sinθc= 1.12/1.20 θc= 69° 90-69 = 21°
Diamond has an index of refraction of 2.419. What is the critical angle for internal reflection inside a diamond that is in air?
24.4° 1sin90°=2.419sinθ sinθ = invsin(1/2.419)
A ray of light strikes a thick sheet of glass (n = 1.5) at an angle of 25° with the normal. Find the angle of the ray REFLECTED off the glass surface with respect to the normal.
25 ° angle of reflection=angle of incidence
An underwater scuba diver sees the Sun at an apparent angle of 41.0° from the vertical. What is actual direction of the Sun?
29° above horizon n1 sin θ1= n2 sin θ2 θ1 = invsin (1.333 sin(41.0°)) θ1= 61° 90°-θ = 29°
Helium-neon laser light has a wavelength in air of 632.8 nm. What is the energy of a single photon in the beam? (h = 6.626x 10^-34 Js and c = 3.00 x10^8 m/s)
3.14x10^-19J E=hc/λ E= ((6.62x10^-34)(3x10^8))/(632.8x10^-9)
Carbon tetrachloride (n = 1.46) is poured into a container made of crown glass (n = 1.52). If the light ray in glass incident on the glass-to-liquid boundary makes an angle of 30 degrees with the normal, what is the angle of the corresponding refracted ray with respect to the normal?
31.4 ° ni(sinθi) = nr(sinθr) ni =1.52 (in glass), Theta i=30 degrees (angle in glass), nr =1.46 (in carbon tetrachloride) 1.52(sin(30))= 1.46(sinθr) [1.52(sin(30))]/1.46 = sin(θr) 0.5205 = sin(θr) θr = invsine(0.5205) = 31.4 degrees
If light from a 560-nm monochromatic source in air is incident upon the surface of fused quartz (n=1.56) at angle of 60 degrees, what is the wave length of the ray refracted within the quartz?
359 nm λ2=λ1(n1/n2) λ2=560(1/1.56)
A beam of light in air is incident at an angle of 35 degrees to the surface of a rectangular block of clear plastic (n = 1.5). The light beam first passes through the block and reemerges from the opposite side into air at what angle to the normal to that surface?
35° The light ray bends towards the normal upon entering and away from the normal upon exiting. If the opposite sides are parallel to each other and surrounded by the same material, then the angle at which the light enters is equal to the angle at which the light exits.
The light beam shown in the figure below makes an angle of ϕ = 22.8° with the normal line NN' in the linseed oil. Determine the angles θ and θ'. (The refractive index for linseed oil is 1.48.)
35° θ1=invsin((n2)(sinθ2)/n1) θ1= invsin[(1.48)(sin22.8)/1.00] 25.5° θ2=invsin((n2)(sinθ2)/n1) θ2= invsin[(1.48)(sin22.8)/1.33]
A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 26.5° and the angle of refraction is 15.3°, find the critical angle for the liquid when surrounded by air.
36.2° n1sinθ1=n2sinθ2 1sin25.6=n2sin15.3 n2=sin26.5/sin15.3 =1.69 sinθc=n1/n2 sinθc=1/1.691 = .59 invsin(.59) =36.2
A monochromatic beam of light in air has a wavelength of 589 nm in air. It passes through glass (n = 1.52) and then through carbondisulfide (n=1.63). What is its wavelength in the carbondisulfide?
361 nm fλ=c λcs=λ/ncs2 λcs= 589/1.63
A ray of light is incident on a liquid-to-glass interface at an angle of 35 degrees. Indices of refraction for the liquid and glass are, respectively, 1.63 and 1.52. What is the angle of refraction for the ray moving through the glass?
38° 1.63sin35°=1.52sinθ2 θ2=invsin(1.63sin35°/1.52)
What is the wavelength of 100 MHz FM radio electromagnetic waves?
3m λ=c/f λ= (3x10^8)/10^8
A radar pulse returns 3.0 x 10^-4 seconds after it is sent out, having been reflected by an object. What is the distance between the radar antenna and the object? (c = 3.00 x 10^8 m/s)
4.5x10^4 m Δx= cΔt =(3 x 10^8 m/s)(3x10^-4 s) =9x10^4 m L= Δx/2 =4.5x10^4 m
What is the angle of incidence on an air-to-glass boundary if the angle of refraction in the glass (n = 1.52) is 25 degrees?
40° 1.52 (sin(25)) = 1.00(sine(Theta r) 1.52 * sine(25 degrees)/1.00 = sinθr 0.6424 = sinθr θr = invsine(0.6424) = 40.0 degrees
A fish is 1.2 m beneath the surface of a still pond of water. At what maximum angle can the fish look toward the surface (measured with respect to the normal to the surface) in order to see a fisherman sitting on a distant bank? (for water, n = 1.333)
48.6 ° θc= invsin(1/1.333)
Two mirrors make an angle of 30°. A ray of light enters the system and is reflected once off each mirror in a symmetrical manner (the angles of incidence for the two reflections are the same). Through what angle is the ray turned?
60° 90°-30°
A fiber optic line is composed of a core with an index of refraction of 1.47 and cladding with an index of 1.31. Which one of the following relations best describes angles of incidence θ that will result in total internal reflection within the fiber optic line?
63 ° θ= invsin(n1/n2) θ= invsin(1.31/1.47)
A container of flint glass (n = 1.66) holds a small quantity of benzene (n = 1.501). What is the critical angle for internal reflection of a ray in the glass when it is incident on the glass-to-liquid surface?
64.7° sinθc=n1/n2 sinθc= 1.501/1.66
Carbon disulfide (n = 1.63) is poured into a container made of crown glass (n = 1.52). What is the critical angle for internal reflection of a ray in the liquid when it is incident on the liquid-to-glass surface?
68.8 ° 1.63(sinθc) = 1.52(sin (90)) sinθc = 1.52/1.63 = 0.9325 inversesin(0.9325) = 68.8 degrees
An ultraviolet light has a wavelength of 300 nm and a speed of 2.1x10^8 m/s through a transparent medium. What is the frequency of this wave in the medium?
7x10^14 Hz f=v/λ f= (2.1x10^8 m/s)/(300x10^-9)
The ionization energy of the hydrogen atom is 13.6 eV. What is the wavelength of the photon having this much energy? (h=6.63x10^-34Js, c= 3.00x10^6 m/s, 1eV= 1.60x10^-19 J, 1nm= 10^-9)
91.4 m E=hc/λ λ= hc/E λ=(6.63x10^-34)(3x10^8)/((13.6)(1.6*10^-19)) =9.14x10^-8m =91.4nm
Dispersion occurs when:
A material slows down some wavelengths more than others Dispersion occurs when a single material bends certain colors of light more than other colors of light. The cause is the fact that different colors of light have different speeds within the same material.
Refraction
Changing direction when crossing a boundary
In order of increasing frequency, which of the following is correct?
Infrared, visible, ultraviolet and gamma
One phenomenon that demonstrates the wave nature of light is:
Interference effects because it only happens with waves
A light ray incident on the interface between air and glass can undergo total internal reflection:
Only in the glass
Blue light with a wavelength of 425 nm passes from a vacuum into a glass lens; and the index fraction is found to be 1.65. The glass lens is replaced with a plastic lens. The index fraction for the plastic lens is 1.54. In which one of the two lenses does the light have the greatest speed and what is the speed?
Plastic= 1.95x10^8 m/s v= c/n v= (3.0x10^8 m/s)/ 1.54
When light from air hits a smooth piece of glass (n= 1.5) with the ray perpendicular to the glass surface, which of the following will occur?
Reflection and transmission at an angle of 0°
