Q: A thin film of oil ($$n=1.40) $$floats on water ($$n=1.33). $$For which minimum nonzero thickness will there be constructive interference for reflected light of wavelength $$560\ \text{nm} in $$air?

$$t = \dfrac{560\ \text{nm}}{4 \times 1.40}$$

Q: A diffraction grating has 1000 lines per mm. What is the angular separation between the first-order maxima for wavelengths $$\$$lambda_1$$ = 400\ \text{nm}$$ and $$\$$lambda_2$$ = 700\ \text{nm}$$?

$$\Delta \theta \approx 20.8^\circ$$

Q: A telescope has an objective lens of diameter $$D$$ and is used to observe light of wavelength $$\lambda. $$According to the Rayleigh criterion, what is the minimum angular separation $$\theta_{min}$$ that can be resolved?

$$\theta_{min} = 1.22 \dfrac{\lambda}{D}$$

Question 1

A sinusoidal wave is described by the equation $$y(x, t) = A \sin(kx - \omega t). If $$the amplitude $$A is $$doubled, what happens to the energy carried by the wave?

Accepted Answer

The energy is quadrupled.

Question 2

Which of the following best describes the relationship between the electric field $$E$$ and magnetic field $$B in an $$electromagnetic wave propagating in vacuum?

Accepted Answer

They are perpendicular to each other and to the direction of propagation.

Question 3

A radio station broadcasts at a frequency of $$100\ 	ext{MHz}. $$What is the wavelength of these radio waves in air? (Speed of light $$c = 3 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

$$30\ 	ext{m}$$

Question 4

A beam of light passes from air ($$n=1.00) $$into water ($$n=1.33) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction in the water?

Accepted Answer

$$22.1^\circ$$

Question 5

Which of the following statements about total internal reflection is correct?

Accepted Answer

It occurs when light travels from a medium with higher refractive index to one with lower refractive index and the angle of incidence exceeds the critical angle.

Question 6

A thin film of oil ($$n=1.40) $$floats on water ($$n=1.33). $$For which minimum nonzero thickness will there be constructive interference for reflected light of wavelength $$560\ 	ext{nm} in $$air?

Accepted Answer

$$t = \dfrac{560\ 	ext{nm}}{4 	imes 1.40}$$

Question 7

A diffraction grating has 1000 lines per mm. What is the angular separation between the first-order maxima for wavelengths $$\$$lambda_1$$ = 400\ 	ext{nm}$$ and $$\$$lambda_2$$ = 700\ 	ext{nm}$$?

Accepted Answer

$$\Delta 	heta \approx 20.8^\circ$$

Question 8

A lens with a focal length of $$0.25\ 	ext{m} is $$used as a magnifier. What is its power in diopters?

Accepted Answer

$$4\ 	ext{D}$$

Question 9

Unpolarized light of intensity $$I_0$$ passes through two ideal polarizers. The transmission axis of the second polarizer is at $$60^\circ to $$the first. What is the intensity of the transmitted light?

Accepted Answer

$$I_0/8$

Question 10

A single slit of width $$a is $$illuminated by light of wavelength $$\lambda. $$The first minimum in the diffraction pattern occurs at an angle $$	heta$$ such that $$a \sin 	heta = \lambda. If $$the slit width is halved, what happens to the angular width of the central maximum?

Accepted Answer

It is doubled.

Question 11

A beam of white light passes through a prism. Which color is deviated the most and why?

Accepted Answer

Violet, because it has the shortest wavelength and higher refractive index.

Question 12

A telescope has an objective lens of diameter $$D$$ and is used to observe light of wavelength $$\lambda. $$According to the Rayleigh criterion, what is the minimum angular separation $$	heta_{min}$$ that can be resolved?

Accepted Answer

$$	heta_{min} = 1.22 \dfrac{\lambda}{D}$$

Question 13

A person with a near point of $$100\ 	ext{cm}$$ wants to read a book at $$25\ 	ext{cm}. $$What power lens (in diopters) should be prescribed?

Accepted Answer

$$+3.0\ 	ext{D}$$

Question 14

In Young’s double-slit experiment, the distance between the slits is $$0.5\ 	ext{mm}$$ and the screen is $$2\ 	ext{m}$$ away. If the wavelength of light is $$500\ 	ext{nm}$$, what is the distance between adjacent bright fringes?

Accepted Answer

$$2\ 	ext{mm}$$

Question 15

A He-Ne laser emits light at $$633\ 	ext{nm}$$ with a power of $$0.5\ 	ext{mW}$$ over a beam diameter of $$1.0\ 	ext{mm}. $$What is the intensity of the beam?

Accepted Answer

$$637\ 	ext{W/m}^2$$

Question 16

Which of the following best explains why the sky appears blue during the day?

Accepted Answer

Blue light is scattered more than red light due to its shorter wavelength.

Question 17

A point source emits electromagnetic waves uniformly in all directions with a total power $$P. At a $$distance $$r$$ from the source, what is the intensity $$I$$?

Accepted Answer

$$I = \dfrac{P}{4\pi r^2$}$$

Question 18

A monochromatic light source of wavelength $$700\ 	ext{nm}$$ and power $$60\ 	ext{W}$$ radiates uniformly in all directions. What is the maximum electric field amplitude $$E_{max} at a $$distance of $$5.0\ 	ext{m}$$ from the source?

Accepted Answer

$$E_{max} = 673\ 	ext{V/m}$$

Electromagnetic Waves, Geometric Optics, and Wave Phenomena

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