Unit 4: The Wave Nature of Light
Unit Test
Version A
Good Luck!
Name: __________________________________________
Date: ___________________________________________
Modality
Marks
Knowledge
/26
Communication
/6
Knowledge: 26 marks total
Part A: Multiple choice (1 mark each). Identify the letter of the choice that best completes
the statement or answers the question
1. The reason there are two slits, rather than one, in a Young’s double slit experiment is:
a) to increase the intensity
b) one slit is for frequency, the other for wavelength
c) to create a path length difference
d) one slit is for electric fields, the other is for magnetic fields
e) two slits in parallel offer less resistance
2. In a Young’s double-slit experiment the center of a bright fringe occurs wherever waves
from the slits differ in phase by a multiple of:
a) π/4
b) π /2
c) π
d) 3π /4
e) 2π
3. Light must travel as a transverse wave because it
a) can be polarized
b) can travel through a vacuum
c) slows down and bends toward the normal
d) undergoes diffraction
e) disperses when travelling through a glass prism
4. Monochromatic light, at normal incidence, strikes a thin film in air. If λ denotes the
wavelength of light, what is the thinnest film in which the reflected light will be a
maximum?
a) much less than λ
b) λ/4
c) λ/2
d) 3λ/4
e) λ
5. A series of wave fronts in a wave tank are travelling toward an opening. Which of the
following changes would cause an increase in the amount of diffraction?
a) decreasing the amplitude of the wave
b) decreasing the frequency of the wave
c) increase the size of the opening
d) placing the wave generator closer to the opening
e) using a shorter wavelength
6. As more slits with the same spacing are added to a diffraction grating the lines:
a) spread further apart
b) move closer together
c) become wider
d) becomes narrower
e) does not change in position or width
7. In which of the following can the property of polarization not be used?
a) analyze the stress distribution in materials
b) improve picture quality in photographs
c) reducing glare from the sun
d) identifying solution concentrations
e) measuring very small distances using interference patterns
8. Which of the following lists the electromagnetic radiation in order from shortest
wavelength to longest wavelength?
a) infrared radiation, microwaves, ultraviolet radiation, x rays
b) x rays, microwaves, infrared radiation, ultraviolet radiation
c) infrared radiation, ultraviolet radiation, microwaves, x rays
d) microwaves, infrared radiation, ultraviolet radiation, x rays
e) x rays, ultraviolet radiation, infrared radiation, microwaves
9. The index of refraction of benzene is 1.80. The critical angle for total internal reflection,
at a benzene-air interface, is about:
a) 56°
b) 47°
c) 34°
d) 22°
e) 18°
10. The separation of white light into colors by a prism is associated with:
a) total internal reflection
b) partial reflection from each surface
c) variation of index of refraction with wavelength
d) a decrease in the speed of light in the glass
e) selective absorption of various colors
Part B: Problems. Please show all your work.
11. A soap bubble 250 nm thick is illuminated by white light. The index of refraction of the
soap film is 1.36.
a) Which colors are not seen in the reflected light? (5 marks)
Solution:
The colors of light that are not seen would have undergone destructive interference. The
condition for destructive interference is:
l=
2nt
m
We can check the destructive interference condition for the first three orders (i.e. m = 1, 2,
3):
(2)(1.36)(250 ´10-9 )
= 680nm
(1)
(2)(1.36)(250 ´10-9 )
l2 =
= 340nm
(2)
(2)(1.36)(250 ´10-9 )
l3 =
= 227nm
(3)
l1 =
680 nm lies in the red region of the spectrum, whereas 340 nm and 227 nm lie in the
ultraviolet region of the spectrum, and is, therefore, invisible to the human eye. Therefore,
the only non-reflected color is red.
b) What color does the soap film appear at normal incidence? (5 marks)
Solution:
The colors of light that are not seen would have undergone destructive interference. The
condition for destructive interference is:
l=
2nt
m +1/ 2
We can check the destructive interference condition for the first three orders (i.e. m = 0, 1,
2):
l1 =
(2)(1.36)(250 ´10-9 )
=1360nm
(1/ 2)
l2 =
(2)(1.36)(250 ´10-9 )
= 453nm
(3 / 2)
l3 =
(2)(1.36)(250 ´10-9 )
= 272nm
(5 / 2)
1360 nm lies in the infrared region of the spectrum, 453 nm lies in the blue region of the
spectrum, and 272 nm lie in the ultraviolet region of the spectrum, and 272 nm lies in the
ultraviolet region of the spectrum. Both 1360 nm and 272 nm are invisible to the human
eye. Therefore, the soap bubble will appear blue.
12. A two-point source interference pattern is generated in a swimming pool. A piece of
Styrofoam, located on the second nodal line, is 12.0 m from one source and 20.0 m from
the other source. One wave crest takes 2.0 s to travel the 35.0 m width of the pool. Find the
speed, wavelength, and frequency of the waves (6 marks).
Solution:
The speed of the waves can be found as follows:
n=
d 35.0m
=
=17.5m / s
t
2.0s
\n =18m / s
The wavelength of the waves can be found as follows:
P1S1 - P2 S2 = (n -1/ 2)l
l=
12.0m - 20.0m
= 5.333m
2 -1/ 2
\ l = 5.33m
The frequency of the waves can be found as follows:
f=
n 17.5m / s
=
= 3.281Hz
l 5.333m
\ f = 3.3Hz
Communication: 6 marks total
13. In point from, describe how polarized light can be produced from unpolarized light using
the method of selective absorption (6 marks).
Solution:



A polarizer (e.g. Polaroid) is a material that allows only light with an electric field
along a single direction to pass.
When unpolarized light passes through a polarizer, components of the electric field
that are perpendicular to the transmission axis of the polarizer are absorbed by
molecules, which are oriented in the same direction as the oscillating electric field.
Whereas, components of the electric field that are parallel to the transmission axis
are transmitted.
The resulting light that passes through the film is linearly polarized.
Unit 4: The Wave Nature of Light
Unit Test
Version B
Good Luck!
Name: __________________________________________
Date: ___________________________________________
Modality
Marks
Knowledge
/25
Communication
/8
Knowledge: 25 marks total
Part A: Multiple choice (1 mark each). Identify the letter of the choice that best completes
the statement or answers the question
1. Water waves in the sea are observed to have a wavelength of 300 m and a frequency of
0.07 Hz. The speed of these waves is:
f) 0.00023 m/s
g) 2.1 m/s
h) 21 m /s
i) 210 m/s
j) 4286 m/s
2. As used in the laws of reflection and refraction, the “normal” direction is:
f) any convenient direction
g) tangent to the surface
h) along the incident ray
i) perpendicular to the electric field vector of the light
j) perpendicular to the interface
3. If water has an index of refraction of 1.50 and glass has an index of refraction of 1.33,
then total internal reflection at an interface between glass and water:
f) occurs whenever the light goes from glass to water
g) occurs whenever the light goes from water to glass
h) may occur when the light goes from glass to water
i) may occur when the light goes from water to glass
j) can never occur at this interface
4. In a Young’s double-slit experiment, light of wavelength 500 nm illuminates two slits
that are separated by 1 mm. The separation between adjacent bright fringes on a screen 5
m from the slits is
f) 0.10 cm
g) 0.25 cm
h) 0.50 cm
i) 1.0 cm
j) none of the above
5. A glass lens (n = 1.6) is coated with a thin film (n = 1.3) to reduce reflection of certain
incident light. If λ is the wavelength of the light in the film, the least film thickness is:
f) less than λ/4
g) λ/4
h) λ/2
i) λ
j) more than λ
6. The rainbow seen after a rain shower is caused by:
f) diffraction
g) refraction
h) interference
i) polarization
j) absorption
7. In the equation d sinθ = mλ for the lines of a diffraction grating, the symbol m
represents:
f) the number of slits
g) the slit width
h) the slit separation
i) the order of the line
j) the index of refraction
8. Which of the following electromagnetic radiations has photons with the greatest
energy?
f) blue light
g) yellow light
h) x rays
i) radio waves
j) microwaves
9. The wavelength of light beam A is twice the wavelength of light beam B. The energy of
a photon in beam A is:
f) half the energy of a photon in beam B
g) one-fourth the energy of a photon in beam B
h) equal to the energy of a photon in beam B
i) twice the energy of a photon in beam B
j) four times the energy of a photon in beam B
10. Polarization experiments provide evidence that light is:
f) a longitudinal wave
g) a stream of particles
h) a transverse wave
i) some type of wave
j) nearly monochromatic
Part B: Problems. Please show all your work.
11. A student performs Young's double-slit experiment using a slit separation of
21.6 μm. A screen is placed 2.50 m from the centre of the sources. A point on the
fifth nodal line is 37.5 cm from the centre of the interference pattern. Find the
wavelength of the light used. What color of light is this? (5 marks)
Solution:
Given:
n = 5, L = 2.50 m, d = 21.6 μm, x5 = 37.5 cm
Required:
λ=?
In a double-slit experiment, the bright fringes occur when light waves from the
two slits interfere constructively. This happens when the path difference is equal
to a whole number of wavelengths:
sinq =
(n -1/ 2)l xn
=
d
L
l=
l=
xn d
L(n -1 / 2)
(0.375m)(21.6 ´10-6 m)
(2.50m)(4.5)
\ l = 720nm
This wavelength of 720 nm corresponds to red light.
12. Randomly polarized light of wavelength 450 nm is moving through air
(n=1.00).
a) Determine the frequency of the electromagnetic radiation (2 marks).
Solution:
f=
n 3.0 ´108 m / s
=
= 6.67 ´1014 Hz
l 450 ´10-9 m
\ f = 6.7´1014 Hz
b) An incident ray of this light reflects off a pool of water (n = 1.33). An
analyzer determines that the intensity of the reflected light is exactly half
the intensity of the incident light. Determine the angle of incidence (4
marks).
Solution:
The incident ray of light must have been polarized by reflection, since the
intensity of the reflected light was exactly one half the initial intensity. Thus, we
need to determine Brewster’s Angle:
n
tanq B = 2
n1
q B = tan-1 (1.33 /1.00) = 53o
Therefore, the angle of incidence was 53 degrees.
c) As this light reflects off the pool of water, is there an angle of incidence for
which there will be no reflected light? (4 marks)
Solution:
For there to be no reflected light, all the light must be totally internally reflected.
To determine the angle of incidence at which total internal reflection occurs, we
must determine the critical angle:
n
sin qC = 2
n1
However, it’s not possible to get total internal reflection when light passes from a
boundary with a lower index of refraction (air) to a medium with a higher index of
refraction (water). This can also be seen mathematically as follows:
qC = sin-1 (1.33 /1.00)
Therefore, there is no angle of incidence that would result in no reflected light for
light that passes from air to water.
Communication: 8 marks total
13. In point form, describe the following properties of light using Newton’s
Particle Theory of Light:
a) rectilinear propagation (2 marks)
Solution:


Light does not appear to curve, but rather travels in a straight line.
Thus, light must consist of particles moving with extremely high speeds.
b) diffraction (2 marks)
Solution:


Light cannot travel around corners as waves do.
Grimaldi’s observations were a result of collisions between light particles
at the edges of the slit, rather than from light waves spreading out.
c) reflection (2 marks)
Solution:


If light particles undergo completely elastic collisions, the law of
reflection follows from the laws of motion.
Horizontal velocity does not change, but vertical velocity is reversed,
causing the light particles to reverse.
d) refraction (2 marks)
Solution:

Light particles will bend towards the normal if their speed increases.

Light particles accelerate at the boundary as they pass from one medium
to another.