Principles of Optics

Which is the correct relationship for the speed (v) of the following three electromagnetic waves in vacuum? The waves are : $\mathrm{X}$-rays, UV rays, microwaves.

(A) $v_{\text{X-Ray}}$ $<$ $v_{\text{Microwave}}$ $<$ $v_{\text{UV-Ray}}$

(B) $v_{\text{Microwave}}$ $<$ $v_{\text{UV-Ray}}$ $<$ $v_{\text{X-Ray}}$

(C) $v_{\text{X-Ray}}$ $=$ $v_{\text{Microwave}}$ $=$ $v_{\text{UV-Ray}}$

(D) $v_{\text{UV-Ray}}$ $<$ $v_{\text{Microwave}}$ $<$ $v_{\text{X-Ray}}$

(E) $v_{\text{X-Ray}}$ $<$ $v_{\text{UV-Ray}}$ $<$ $v_{\text{Microwave}}$

Chromatic aberration from a lens is a consequence of

(A) polarization.

(B) interference.

(C) total internal reflection.

(D) diffraction.

(E) dispersion.

An ideal green pigment is mixed with an ideal red pigment. After mixing, which one of the following choices best represents the color of the pigment produced?

(A) Blue
(B) Cyan
(C) Magenta
(D) Yellow
(E) Black

An electromagnetic wave has a magnetic field given by the expression (in Cartesian coordinates) $\vec{B}(x,\ y,\ z,\ \mathrm{t})=(6.0\times 10^{-6})\cos(2.21\times 10^{7}z-6.63\times 10^{15}\mathrm{t})\hat{\chi}$. At time $r=0$ and position $\chi=y=z=0$, what is the direction of the electric field associated with this wave?

(A) $+x$
(B) $-x$
(C) $+y$
(D) $-y$
(E) $+z$

A ray of light passes straight downward through the point labeled $\mathrm{B}$ in the diagram shown. The ray reaches a flat mirror placed at an angle $\theta$ to the horizontal as shown. Which one of the locations labeled in the figure best represents the point through which the ray reflected from the mirror will pass?

(A) $\mathrm{A}$

(B) $\mathrm{B}$

(C) $\mathrm{C}$

(D) $\mathrm{D}$

(E) $\mathrm{E}$

Electromagnetic radiation travels through vacuum with a wavelength of 400 $nm$. Which one of the following choices best describes this type of radiation?

(A) $\mathrm{X}$-rays
(B) Radio Waves
(C) Microwaves
(D) Red Light
(E) Violet Light

Coherent light of wavelength 550 $nm$ shines on a double slit apparatus that has point slits spaced by a distance of 42.4 $\mu m$. In theory, what is the maximum order bright fringe that can be viewed?

(A) 1297
(B) 77
(C) 12
(D) 8
(E) 1

A beam of unpolarized light traveling in air strikes a piece of optically flat glass at an angle of incidence of $58^{\mathrm{o}}$. Some of the light is reflected while the remainder is transmitted into the glass. The reflected beam is 100% polarized parallel to the surface of the glass. What is the index of refraction for the glass?

(A) 1.60
(B) 1.53
(C) 1.47
(D) 1.38
(E) 1.18

Which one of the following statements best describes Huygens's Principle?

(A) An additional pressure is transmitted undiminished to all points in the fluid and to the walls of the container.

(B) Each point on a wavefront acts as a source of secondary spherical wavelets (new waves).

(C) For every action force, there is an equal but opposite reaction force.

(D) It is impossible to have a process which has the sole result of transferring energy from a low temperature reservoir to a high temperature reservoir.

(E) A time-changing magnetic field has an associated induced electric field.

Light of wavelength 600 $nm$ is transmitted from air into a piece of glass. Which one of the labeled arrows best indicates the path of the light ray after it enters the glass?

(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) $\mathrm{D}$
(E) $\mathrm{E}$

It is observed that a light ray changes direction when it enters a new material. Which one of the following choices is the term best associated with this phenomenon?

(A) Doppler Effect
(B) Interference
(C) Polarization
(D) Diffraction
(E) Refraction

Plane-polarized light with intensity $I$ is incident on a single polarizing sheet. If the intensity of the light become $\displaystyle \frac{1}{4} I$ after passing through the polarizer, what is the angle between the transmission axis of the polarizer and the polarization plane of the incident light?

(A) $75^{\circ}$
(B) $67.5^{\circ}$
(C) $60^{\circ}$
(D) $30^{\circ}$
(E) $22.5^{\circ}$

A ray of monochromatic light enters the right-triangular glass as shown. The glass has an index of refraction of 2.00 and it is surrounded by air. Which one of the lettered rays shows the path of the light after it exits the glass?

(A) $\mathrm{A}$

(B) $\mathrm{B}$

(C) $\mathrm{C}$

(D) $\mathrm{D}$

(E) $\mathrm{E}$

A laser beam with wavelength 632.8 $nm$ shines onto a newly fabricated single slit. As a result, the width of the principal bright region on a viewing screen 1.25 $m$ away is 1.00 $m$. Which one of the following best represents the size of the single slit opening?

(A) 0.79 $\mu m$
(B) 0.85 $\mu m$
(C) 1.01 $\mu m$
(D) 1.58 $\mu m$
(E) 1.70 $\mu m$

A thin film of alcohol $(n_{alcohol}=1.35)$ lies on a flat glass surface $(n_{glass}=1.60)$. When light of wavelength 540 $nm$ is incident normal to the alcohol surface from air, the light is strongly reflected, but when light of wavelength 432 $nm$ is incident normal to the surface from air, the reflected light is minimized. Which one of the following choices could represent the thickness, $t$, of the alcohol film?

(A) 216 $nm$
(B) 320 $nm$
(C) 324 $nm$
(D) 400 $nm$
(E) 486 $nm$

Which one of the following choices best describes what it means for an object to be iridescent?

(A) The color of the object appears to change with a change in the angle of view.

(B) The object appears to have two images formed from it because of differences in index of refraction.

(C) The color of the object appears to be different based on its temperature.

(D) The object remains illuminated after turning off all surrounding light sources.

(E) The object is alive and producing light biochemically.

Which one of the following choices best represents the type of electromagnetic wave associated with a frequency of $10^{18}Hz$?

(A) AM radio
(B) microwaves
(C) ultraviolet light
(D) X rays
(E) red light

An object appears green when ideal cyan light shines on it. If ideal yellow light were to shine on the object, which one of the following choices identifies the color(s) that the object could appear?

(A) only red

(B) only yellow

(C) only green or black

(D) only yellow or green

(E) only yellow, green, or red

Pure red light shines through a diffraction grating of1200 $\displaystyle \frac{lines}{cm}$ and produces an interference pattern on a screen a distance 5.0 $m$ away. Which one of the following choices best represents the distance between the first and third principal bright spots on the screen?

(A) 0.02 $m$
(B) 0.10 $m$
(C) 1.0 $m$
(D) 2.0 $m$
(E) 4.0 $m$

Why does the sky appear to be more blue when looking directly overhead than it does when looking toward the horizon?

(A) The atmosphere is denser at higher altitude than it is at the $\mathrm{E}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}^{\dagger}\mathrm{s}$ surface.

(B) The temperature of the upper atmosphere is higher than it is at the $\mathrm{E}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}^{\dagger}\mathrm{s}$ surface.

(C) There are fewer clouds directly overhead than near the horizon.

(D) The sunlight travels over a longer path at the horizon, resulting in more scattering.

(E) The sunlight entering the atmosphere from directly above undergoes greater refraction and

dispersion.

In August of 2017, the gravitational waves from the collision and merger of two neutron stars were detected. After their collision, several forms of electromagnetic radiation were subsequently detected. What was the first type of electromagnetic radiation detected after the gravitational waves were detected?

(A) Gamma rays
(B) Visible light
(C) Radio waves
(D) $\mathrm{X}$-rays
(E) Microwaves

The red glow in the neon tube of an advertising sign is a result of (A) fluorescence
(B) incandescence
(C) iridescence
(D) coherence
(E) de-excitation

A 15.0-mW laser emits a beam that is 2.00 mm in diameter. What is the intensity of this beam?

(A) 1.19 $\mathrm{x}10^{3}\mathrm{W}/\mathrm{m}^{2}$

(B) 1.19 $\mathrm{x}10^{4}\mathrm{W}/\mathrm{m}^{2}$

(C) 3.59 $\mathrm{x}10^{4}\mathrm{W}/\mathrm{m}^{2}$

(D) 4.77 $\mathrm{x}10^{4}\mathrm{W}/\mathrm{m}^{2}$

(E) 2.98 $\mathrm{x}10^{5}\mathrm{W}/\mathrm{m}^{2}$

Which of the following colors of visible light has the longest wavelength?
(A) Violet
(B) Yellow
(C) Blue
(D) Green
(E) Red

Two light waves, initially emitted in phase, will interfere constructively with maximum amplitude if the path-length difference between them is:
(A) 1.5 wavelengths
(B) one wavelength
(C) one-half wavelength
(D) one-quarter wavelength
(E) one-eighth wavelength

A thick glass plate has parallel sides. A beam of white light is incident on one side at an angle between $0^{\circ}$ and $90^{\circ}$ with the normal. Which color emerges from the other side first?
(A) All of them
(B) Red
(C) Green
(D) Violet
(E) None of them

A triangular glass prism $(\mathrm{n}=1.6)$ is immersed in a liquid $(\mathrm{n}=1.1)$ as shown. A laser light is incident as shown on face $A B$ making an angle of $20^{\circ}$ with the normal $(N)$. Calculate the angle that the ray emerging from $A C$ makes with the ground when it leaves $A C$ and strikes the ground.

(A) $28.1^{\circ}$
(B) $30.3^{\circ}$
(C) $33.8^{\circ}$
(D) $36.1^{\circ}$
(E) $18.9^{\circ}$

Light is refracted when it passes from air into glass. Which of these wave properties changes?
(A) Speed only
(B) Wavelength only
(C) Frequency only
(D) Both speed and wavelength
(E) Both speed and frequency

An object is placed in front of a convex lens at a distance less than $F$. The image produced by the lens is...
(A) real, inverted, and smaller than the object.
(B) real, inverted, and larger than the object.
(C) virtual, upright, and larger than the object.
(D) virtual, upright, and smaller than the object.
(E) virtual, inverted, and larger than the object.