Q: A diffraction grating has 600 lines/mm. What is the distance $$d$$ between adjacent slits?

$$d = 1.67 \times 10$$^{-6}$$ m

Q: Which of the following best explains why the maximum order $$m_{max}$$ for a diffraction grating is limited?

Because $$\sin \theta$$ cannot exceed 1, so $$m_{max} \u003c \frac{d}{\lambda}$$

Question 1

When a light wave traveling in air strikes a glass surface (higher index of refraction), what happens to the phase of the reflected wave?

Accepted Answer

It undergoes a phase change of $$\pi.$$

Question 2

A soap bubble (n = 1.33) in air has a wall thickness of 115 nm. What visible color is most strongly reflected? (Assume constructive interference and normal incidence, $$\lambda_{air}$$ for visible light: 400–700 nm)

Accepted Answer

Red ($$\lambda \approx 610 nm)$$

Question 3

Which equation gives the condition for constructive interference in a thin film when there is a half-cycle phase shift upon reflection?

Accepted Answer

$$2t = (m + \frac{1}{2})\lambda_n$$

Question 4

A thin oil film (n = 1.45) on water (n = 1.33) is illuminated at normal incidence with white light. The film is 280 nm thick. What is the wavelength in air of the light most strongly reflected?

Accepted Answer

Question 5

Which of the following best describes the effect of a thin transparent film on a glass lens?

Accepted Answer

It can reduce reflections by causing destructive interference.

Question 6

A diffraction grating has 600 lines/mm. What is the distance $$d$$ between adjacent slits?

Accepted Answer

$$d = 1.67 	imes 10$$^{-6}$$ m

Question 7

For a diffraction grating, which equation gives the angular position $$	heta of $$the $$m-th $$order bright fringe?

Accepted Answer

$$d \sin 	heta = m\lambda$$

Question 8

A transmission grating is illuminated with white light. Which color will appear at the largest angle for the first order ($$m=1) $$maximum?

Accepted Answer

Red

Question 9

A radar-absorbing polymer (n = 1.50) is used to coat an airplane. If radar waves have a wavelength of 3.00 cm, what is the minimum thickness of the coating for destructive interference of reflected waves?

Accepted Answer

$$t = \frac{\lambda}{4n} = 0.5 cm$$

Question 10

In a wedge-shaped air film between two glass plates, 30 dark fringes are observed using 600 nm light. What is the thickness of the air gap at the edge where the wire is placed?

Accepted Answer

$$t = 9.0 \mu m$$

Question 11

Which of the following is NOT a real-world application of thin film interference?

Accepted Answer

Measuring the speed of light in a vacuum

Question 12

A diffraction grating produces a third-order maximum for the 656 nm hydrogen-α line at $$37^\circ. If $$the grating is 2.5 cm wide, how many grooves does it have?

Accepted Answer

9000

Question 13

Which of the following statements about the phase change of light upon reflection is correct?

Accepted Answer

A phase change of $$\pi$$ occurs when light reflects from a medium with a higher index of refraction.

Question 14

In a thin film, what must be true for constructive interference if there is no phase shift upon reflection?

Accepted Answer

$$2t = m\lambda_n$$

Question 15

A transmission grating is used in a spectroscope to measure the angular position of spectral lines. What is the primary purpose of the collimator in this setup?

Accepted Answer

To produce parallel rays of light for accurate diffraction measurements

Question 16

Which of the following best explains why the maximum order $$m_{max}$$ for a diffraction grating is limited?

Accepted Answer

Because $$\sin 	heta$$ cannot exceed 1, so $$m_{max} \u003c \frac{d}{\lambda}$$

Question 17

A thin film of material with index $$n$$ and thickness $$t is $$illuminated at normal incidence. Which equation gives the positions $$x of $$bright fringes in a wedge-shaped film?

Accepted Answer

$$x = \frac{\lambda \ell (m + \frac{1}{2})}{2 n h}$$

Question 18

Which of the following is a key advantage of using a diffraction grating in spectroscopy?

Accepted Answer

It can separate light into its constituent wavelengths with high resolution.

Light Reflection, Transmission, Thin Film Interference, and Diffraction Gratings

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