Question 1

A grating with 8000 slits over $2.54 \mathrm{~cm}$ is illuminated by light of a wavelength of $546 \mathrm{~nm}$. What is the angle for the third-order maximum?

Accepted Answer

A)  $10.5^{\circ}$ 
B)  $15.1^{\circ}$ 
C)  $31.1^{\circ}$ 
D)  $26.3^{\circ}$ 
A)  $10.5^{\circ}$ 
B)  $15.1^{\circ}$ 
C)  $31.1^{\circ}$ 
D)  $26.3^{\circ}$ C

Question 2

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 $\mathrm{cm}$ ?

Accepted Answer

A)  $1.1 \times 10^{-4} \mathrm{rad}$ 
B)  $2.7 \times 10^{-4} \mathrm{rad}$ 
C)  $4.2 \times 10^{-5} \mathrm{rad}$ 
D)  $3.7 \times 10^{-3} \mathrm{rad}$ 
E)  $5.5 \times 10^{-8} \mathrm{rad}$ 
A)  $1.1 \times 10^{-4} \mathrm{rad}$ 
B)  $2.7 \times 10^{-4} \mathrm{rad}$ 
C)  $4.2 \times 10^{-5} \mathrm{rad}$ 
D)  $3.7 \times 10^{-3} \mathrm{rad}$ 
E)  $5.5 \times 10^{-8} \mathrm{rad}$ A

Question 3

What is the limiting angle of resolution, in degrees, for a microscope with an objective $0.50 \mathrm{~cm}$ in diameter when viewing with light of wavelength $590 \mathrm{~nm}$ ?

Accepted Answer

A)  $2.1 \times 10^{-3}$ 
B)  $4.1 \times 10^{-3}$ 
C)  $7.2 \times 10^{-5}$ 
D)  $1.4 \times 10^{-4}$ 
E)  $8.2 \times 10^{-3}$ 
A)  $2.1 \times 10^{-3}$ 
B)  $4.1 \times 10^{-3}$ 
C)  $7.2 \times 10^{-5}$ 
D)  $1.4 \times 10^{-4}$ 
E)  $8.2 \times 10^{-3}$ E

Question 4

What is the angular resolution of the eye at a wavelength of $500 \mathrm{~nm}$ for a pupil diameter of $2.8 \mathrm{~mm}$ ?

Accepted Answer

A)  $3.3 \times 10^{-5} \mathrm{rad}$ 
B)  $2.2 \times 10^{-4} \mathrm{rad}$ 
C)  $4.5 \times 10^{-5} \mathrm{rad}$ 
D)  $8.9 \times 10^{-5} \mathrm{rad}$ 
E)  $1.8 \times 10^{-4} \mathrm{rad}$ 
A)  $3.3 \times 10^{-5} \mathrm{rad}$ 
B)  $2.2 \times 10^{-4} \mathrm{rad}$ 
C)  $4.5 \times 10^{-5} \mathrm{rad}$ 
D)  $8.9 \times 10^{-5} \mathrm{rad}$ 
E)  $1.8 \times 10^{-4} \mathrm{rad}$

Question 5

Two planes of atoms in a crystal are separated by $3.25 \times 10-10 \mathrm{~m}$. Light of what wavelength would show constructive interference at an angle of 17.5 degrees relative to the crystal surface?

Accepted Answer

A)  $1.95 \times 10-10 \mathrm{~m}$ 
B)  $9.75 \times 10^{-10} \mathrm{~m}$ 
C)  $1.46 \times 10^{-10} \mathrm{~m}$ 
D)  $3.9 \times 10-10 \mathrm{~m}$ 
E)  $4.9 \times 10^{-9} \mathrm{~m}$ 
A)  $1.95 \times 10-10 \mathrm{~m}$ 
B)  $9.75 \times 10^{-10} \mathrm{~m}$ 
C)  $1.46 \times 10^{-10} \mathrm{~m}$ 
D)  $3.9 \times 10-10 \mathrm{~m}$ 
E)  $4.9 \times 10^{-9} \mathrm{~m}$

Question 6

If two coherent waves, one with intensity $8.0 I_{0}$ and the other with intensity $4.0 I_{0}$, undergo destructive interference, what is the resulting intensity?

Accepted Answer

A)  $4.0 I_{0}$ 
B)  $0.69 I_{0}$ 
C)  $-4.0 I_{0}$ 
D)  $1.9 I_{0}$ 
E)  $6.0 I_{0}$ 
A)  $4.0 I_{0}$ 
B)  $0.69 I_{0}$ 
C)  $-4.0 I_{0}$ 
D)  $1.9 I_{0}$ 
E)  $6.0 I_{0}$

Question 7

A grating is made with 600 slits per millimeter. What is the slit separation?

Accepted Answer

A)  $916 \mathrm{~nm}$ 
B)  $160 \mathrm{pm}$ 
C)  $600 \mathrm{~nm}$ 
D)  $3.33 \times 10^{-6} \mathrm{~m}$ 
E)  $1.67 \times 10^{-6} \mathrm{~m}$ 
A)  $916 \mathrm{~nm}$ 
B)  $160 \mathrm{pm}$ 
C)  $600 \mathrm{~nm}$ 
D)  $3.33 \times 10^{-6} \mathrm{~m}$ 
E)  $1.67 \times 10^{-6} \mathrm{~m}$

Question 8

A Michelson interferometer is used to measure the index of refraction of a gas by counting interference fringes as the gas is slowly leaked into a transparent vessel placed in one arm of the interferometer. The vessel initially contains a vacuum, and as the gas is let in, the number of bright fringes is counted-i.e., the number of times the central region of the screen changes from bright to dark and back to bright. Suppose the index of refraction of the gas is 1.0003 . If the wavelength of light used is $560 \mathrm{~nm}$, and the vessel containing the gas is $25 \mathrm{~cm}$ long, how many bright fringes will be observed?

Accepted Answer

A)  $1.78 \times 10^{6}$ 
B)  133 
C)  $2.23 \times 10^{5}$ 
D)  $4.47 \times10^{5}$ 
E)  134
F) 267 
A)  $1.78 \times 10^{6}$ 
B)  133 
C)  $2.23 \times 10^{5}$ 
D)  $4.47 \times10^{5}$ 
E)  134
F) 267

Question 9

Substituting $\tan \theta$ for $\sin \theta$ results in what percent error for an angle of $5.00^{\circ}$ ?

Accepted Answer

A)  5.00 
B)  0.191 
C)  0.0333 
D)  0.0166 
E)  0.382 
A)  5.00 
B)  0.191 
C)  0.0333 
D)  0.0166 
E)  0.382

Question 10

Wave 1 has amplitude of $9.0 A_{0}$ and wave 2 has amplitude $4.0 A_{0}$. What is the ratio of their intensities, $I_{1} / I_{2}$ ?

Accepted Answer

A)  5.1 
B)  1.3 
C)  2.3 
D)  1.5 
E)  20 
A)  5.1 
B)  1.3 
C)  2.3 
D)  1.5 
E)  20

Question 11

What minimum thickness of oil $(\mathrm{n}=1.50)$ on the surface of water $(\mathrm{n}=1.33)$ would give destructive interference for $550 \mathrm{~nm}$ light at normal incidence?

Accepted Answer

A)  $78.0 \mathrm{~nm}$ 
B)  $92.0 \mathrm{~nm}$ 
C)  $80.0 \mathrm{~nm}$ 
D)  $275 \mathrm{~nm}$ 
E)  $183 \mathrm{~nm}$ 
A)  $78.0 \mathrm{~nm}$ 
B)  $92.0 \mathrm{~nm}$ 
C)  $80.0 \mathrm{~nm}$ 
D)  $275 \mathrm{~nm}$ 
E)  $183 \mathrm{~nm}$

Question 12

What minimum thickness of oil ( $\mathrm{n}=1.50)$ on the surface of water $(\mathrm{n}=1.33)$ would give constructive interference for $550 \mathrm{~nm}$ light at normal incidence?

Accepted Answer

A)  $92.0 \mathrm{~nm}$ 
B)  $183 \mathrm{~nm}$ 
C)  $80.0 \mathrm{~nm}$ 
D)  $275 \mathrm{~nm}$ 
E)  $78.0 \mathrm{~nm}$ 
A)  $92.0 \mathrm{~nm}$ 
B)  $183 \mathrm{~nm}$ 
C)  $80.0 \mathrm{~nm}$ 
D)  $275 \mathrm{~nm}$ 
E)  $78.0 \mathrm{~nm}$

Question 13

A  Michelson interferometer is used to measure the index of refraction of a gas by counting interference fringes as the gas is slowly leaked into a transparent vessel placed in one arm of the interferometer. The vessel initially contains a vacuum, and as the gas is let in, 397 bright fringes are counted. That is, the central region of the screen changes from bright to dark and back to bright 397 times. If the wavelength of light used is $560 \mathrm{~nm}$, and the vessel containing the gas is $25.0 \mathrm{~cm}$ long, what is the index of refraction of the gas?

Accepted Answer

A)  1.00178 
B)  1.000111 
C)  1.000889 
D)  1.000445 
E)  1.000222 
A)  1.00178 
B)  1.000111 
C)  1.000889 
D)  1.000445 
E)  1.000222

Question 14

Wave 1 has intensity $9.0 I_{0}$ while wave 2 has intensity $4.0 I_{0}$. What is their ratio of amplitudes, $A_{1} / A_{2}$ ?

Accepted Answer

A)  20 
B)  1.3 
C)  2.3 
D)  1.5 
E)  5.1 
A)  20 
B)  1.3 
C)  2.3 
D)  1.5 
E)  5.1

Question 15

A Michelson interferometer can be used to measure very small distances by adjusting the length of one arm while keeping the other arm fixed. As the arm length is slowly changed, the central region of the screen changes from bright to dark and back to bright a number of times, and these bright fringes are counted. Suppose the interferometer uses light of wavelength $560 \mathrm{~nm}$, and as one arm is lengthened by an amount $\Delta \mathrm{x}$, exactly 79 bright fringes are counted. What is the distance $\Delta x$ ?

Accepted Answer

A)  $44.2 \mu \mathrm{m}$ 
B)  $22.1 \mu \mathrm{m}$ 
C)  $7.09 \mathrm{~nm}$ 
D)  $22.4 \mu \mathrm{m}$ 
E)  $44.8 \mu \mathrm{m}$
F) $11.1 \mu \mathrm{m}$ 
A)  $44.2 \mu \mathrm{m}$ 
B)  $22.1 \mu \mathrm{m}$ 
C)  $7.09 \mathrm{~nm}$ 
D)  $22.4 \mu \mathrm{m}$ 
E)  $44.8 \mu \mathrm{m}$
F) $11.1 \mu \mathrm{m}$

Question 16

Light from a HeNe laser (632.8 nm wavelength) is directed upon a straightened strand of human hair, $7.5 \mathrm{~m}$ from the wall. By examining the diffraction pattern produced on the wall, the diameter of the hair can be determined (the diffraction pattern thus produced has minima in the same locations as if the hair were a slit of the same width in an otherwise opaque barrier). If the central diffraction maximum is measured to be $14.6 \mathrm{~cm}$ wide, what is the diameter of the hair?

Accepted Answer

A)  $65 \mu \mathrm{m}$ 
B)  $86.6 \mu \mathrm{m}$ 
C)  $43.3 \mu \mathrm{m}$ 
D)  $32.5 \mu \mathrm{m}$ 
A)  $65 \mu \mathrm{m}$ 
B)  $86.6 \mu \mathrm{m}$ 
C)  $43.3 \mu \mathrm{m}$ 
D)  $32.5 \mu \mathrm{m}$

Question 17

Two coherent waves interfere constructively. One wave has an intensity of $8.00 I_{0}$ and the other has an intensity of $4.00 I_{0}$. What is the intensity of the superposed wave?

Accepted Answer

A)  $23.3 I_{0}$ 
B)  $8.00 I_{0}$ 
C)  $12.0 I_{0}$ 
D)  $4.00 I_{0}$ 
E)  $24.0 I_{0}$ 
A)  $23.3 I_{0}$ 
B)  $8.00 I_{0}$ 
C)  $12.0 I_{0}$ 
D)  $4.00 I_{0}$ 
E)  $24.0 I_{0}$

Question 18

If light of wavelength $690 \mathrm{~nm}$ is used in a double-slit experiment with slit separation $0.206 \mathrm{~mm}$, what angle separates the two fourth-order maxima?

Accepted Answer

A)  $0.768^{\circ}$ 
B)  $3.07^{\circ}$ 
C)  $0.154^{\circ}$ 
D)  $0.307^{\circ}$ 
E)  $1.54^{\circ}$ 
A)  $0.768^{\circ}$ 
B)  $3.07^{\circ}$ 
C)  $0.154^{\circ}$ 
D)  $0.307^{\circ}$ 
E)  $1.54^{\circ}$

Question 19

White light is shone on a very thin layer of mica ( $\mathrm{n}=1.57)$, suspended in air, at normal incidence. When the mica layer is observed from the illuminated side, constructive interference is observed for wavelengths of violet $(400 \mathrm{~nm})$ and yellow $(560 \mathrm{~nm})$ light. What is the thickness of the mica layer?

Accepted Answer

A)  $446 \mathrm{~nm}$ 
B)  $892 \mathrm{~nm}$ 
C)  $700 \mathrm{~nm}$ 
D)  $382 \mathrm{~nm}$ 
E)  $764 \mathrm{~nm}$
F) $600 \mathrm{~nm}$ 
A)  $446 \mathrm{~nm}$ 
B)  $892 \mathrm{~nm}$ 
C)  $700 \mathrm{~nm}$ 
D)  $382 \mathrm{~nm}$ 
E)  $764 \mathrm{~nm}$
F) $600 \mathrm{~nm}$

Question 20

Using a Michelson interferometer and a light source of $400 \mathrm{~nm}$, a change from bright to dark indicates a change in the difference of arm lengths of

Accepted Answer

A)  $1.0 \times 10^{-4} \mathrm{~mm}$. 
B)  $4.0 \times 10^{-4} \mathrm{~mm}$. 
C)  $2.0 \times 10^{-4} \mathrm{~mm}$. 
D)  $3.0 \times 10^{-4} \mathrm{~mm}$. 
A)  $1.0 \times 10^{-4} \mathrm{~mm}$. 
B)  $4.0 \times 10^{-4} \mathrm{~mm}$. 
C)  $2.0 \times 10^{-4} \mathrm{~mm}$. 
D)  $3.0 \times 10^{-4} \mathrm{~mm}$.

Exam 25: Interference and Diffraction

A grating with 8000 slits over 2.54 cm2.54 \mathrm{~cm}2.54 cm is illuminated by light of a wavelength of 546 nm546 \mathrm{~nm}546 nm . What is the angle for the third-order maximum?

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 cm\mathrm{cm}cm ?

What is the limiting angle of resolution, in degrees, for a microscope with an objective 0.50 cm0.50 \mathrm{~cm}0.50 cm in diameter when viewing with light of wavelength 590 nm590 \mathrm{~nm}590 nm ?

What is the angular resolution of the eye at a wavelength of 500 nm500 \mathrm{~nm}500 nm for a pupil diameter of 2.8 mm2.8 \mathrm{~mm}2.8 mm ?

Two planes of atoms in a crystal are separated by 3.25×10−10 m3.25 \times 10-10 \mathrm{~m}3.25×10−10 m . Light of what wavelength would show constructive interference at an angle of 17.5 degrees relative to the crystal surface?

If two coherent waves, one with intensity 8.0I08.0 I_{0}8.0I0​ and the other with intensity 4.0I04.0 I_{0}4.0I0​ , undergo destructive interference, what is the resulting intensity?

A grating is made with 600 slits per millimeter. What is the slit separation?

Substituting tan⁡θ\tan \thetatanθ for sin⁡θ\sin \thetasinθ results in what percent error for an angle of 5.00∘5.00^{\circ}5.00∘ ?

Wave 1 has amplitude of 9.0A09.0 A_{0}9.0A0​ and wave 2 has amplitude 4.0A04.0 A_{0}4.0A0​ . What is the ratio of their intensities, I1/I2I_{1} / I_{2}I1​/I2​ ?

What minimum thickness of oil (n=1.50)(\mathrm{n}=1.50)(n=1.50) on the surface of water (n=1.33)(\mathrm{n}=1.33)(n=1.33) would give destructive interference for 550 nm550 \mathrm{~nm}550 nm light at normal incidence?

What minimum thickness of oil ( n=1.50)\mathrm{n}=1.50)n=1.50) on the surface of water (n=1.33)(\mathrm{n}=1.33)(n=1.33) would give constructive interference for 550 nm550 \mathrm{~nm}550 nm light at normal incidence?

Wave 1 has intensity 9.0I09.0 I_{0}9.0I0​ while wave 2 has intensity 4.0I04.0 I_{0}4.0I0​ . What is their ratio of amplitudes, A1/A2A_{1} / A_{2}A1​/A2​ ?

Two coherent waves interfere constructively. One wave has an intensity of 8.00I08.00 I_{0}8.00I0​ and the other has an intensity of 4.00I04.00 I_{0}4.00I0​ . What is the intensity of the superposed wave?

If light of wavelength 690 nm690 \mathrm{~nm}690 nm is used in a double-slit experiment with slit separation 0.206 mm0.206 \mathrm{~mm}0.206 mm , what angle separates the two fourth-order maxima?

Using a Michelson interferometer and a light source of 400 nm400 \mathrm{~nm}400 nm , a change from bright to dark indicates a change in the difference of arm lengths of

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Filters

A grating with 8000 slits over $2.54 \mathrm{~cm}$ is illuminated by light of a wavelength of $546 \mathrm{~nm}$ . What is the angle for the third-order maximum?

If a laser printer prints at 600 dots per inch, what is the angular separation of the dots when viewed from 40 $\mathrm{cm}$ ?

What is the limiting angle of resolution, in degrees, for a microscope with an objective $0.50 \mathrm{~cm}$ in diameter when viewing with light of wavelength $590 \mathrm{~nm}$ ?

What is the angular resolution of the eye at a wavelength of $500 \mathrm{~nm}$ for a pupil diameter of $2.8 \mathrm{~mm}$ ?

Two planes of atoms in a crystal are separated by $3.25 \times 10-10 \mathrm{~m}$ . Light of what wavelength would show constructive interference at an angle of 17.5 degrees relative to the crystal surface?

If two coherent waves, one with intensity $8.0 I_{0}$ and the other with intensity $4.0 I_{0}$ , undergo destructive interference, what is the resulting intensity?

Substituting $\tan \theta$ for $\sin \theta$ results in what percent error for an angle of $5.00^{\circ}$ ?

Wave 1 has amplitude of $9.0 A_{0}$ and wave 2 has amplitude $4.0 A_{0}$ . What is the ratio of their intensities, $I_{1} / I_{2}$ ?

What minimum thickness of oil $(\mathrm{n}=1.50)$ on the surface of water $(\mathrm{n}=1.33)$ would give destructive interference for $550 \mathrm{~nm}$ light at normal incidence?

What minimum thickness of oil ( $\mathrm{n}=1.50)$ on the surface of water $(\mathrm{n}=1.33)$ would give constructive interference for $550 \mathrm{~nm}$ light at normal incidence?

Wave 1 has intensity $9.0 I_{0}$ while wave 2 has intensity $4.0 I_{0}$ . What is their ratio of amplitudes, $A_{1} / A_{2}$ ?

Two coherent waves interfere constructively. One wave has an intensity of $8.00 I_{0}$ and the other has an intensity of $4.00 I_{0}$ . What is the intensity of the superposed wave?

If light of wavelength $690 \mathrm{~nm}$ is used in a double-slit experiment with slit separation $0.206 \mathrm{~mm}$ , what angle separates the two fourth-order maxima?

Using a Michelson interferometer and a light source of $400 \mathrm{~nm}$ , a change from bright to dark indicates a change in the difference of arm lengths of