Q: A diffraction grating with slit spacing $$d is $$illuminated by monochromatic light of wavelength $$\lambda. At $$what angles $$\theta_m$$ will the principal maxima (bright fringes) appear?

$$d \sin \theta_m = m \lambda$$, where $$m = 0, 1, 2, ...$$

Q: A single slit of width $$a$$ produces a diffraction pattern on a distant screen. At what angles $$\theta$$ will the first minima (dark fringes) occur?

$$a \sin \theta = m \lambda$$, where $$m = 1, 2, 3, ...$$

Question 1

A peacock feather displays vivid colors due to the presence of parallel rods of melanin. What optical phenomenon is primarily responsible for these structural colors?

Accepted Answer

Diffraction and interference from a natural reflection grating

Question 2

A diffraction grating with slit spacing $$d is $$illuminated by monochromatic light of wavelength $$\lambda. At $$what angles $$	heta_m$$ will the principal maxima (bright fringes) appear?

Accepted Answer

$$d \sin 	heta_m = m \lambda$$, where $$m = 0, 1, 2, ...$$

Question 3

A single slit of width $$a$$ produces a diffraction pattern on a distant screen. At what angles $$	heta$$ will the first minima (dark fringes) occur?

Accepted Answer

$$a \sin 	heta = m \lambda$$, where $$m = 1, 2, 3, ...$$

Question 4

In a diffraction grating experiment, the intensity of the principal maxima is given by $$I_{max} = N^2$ I_1$, where N$ is the number of slits and I_1$ is the intensity from a single slit. What happens to the intensity if the number of slits is doubled?

Accepted Answer

The intensity increases by a factor of 4

Question 5

A monochromatic light source is used in a Michelson interferometer. If one mirror is moved by a distance $$\Delta L$$, how many bright fringes $$\Delta m$$ will pass by a reference point?

Accepted Answer

$$\Delta m = 2 \Delta L / \lambda$$

Question 6

Which of the following best explains why a diffraction grating can be used to separate different wavelengths of light?

Accepted Answer

Different wavelengths are diffracted at different angles according to $$d \sin 	heta = m \lambda$$

Question 7

A single-slit diffraction pattern is observed on a screen a distance $$L$$ from the slit. If the slit width $$a is $$decreased, what happens to the width $$w of $$the central maximum?

Accepted Answer

The width increases

Question 8

A double-slit experiment uses slits of finite width $$a$$ separated by distance $$d. $$The resulting intensity pattern is described by the product of two factors. Which equation correctly represents the intensity $$I(y) on $$the screen?

Accepted Answer

$$I(y) = I_0$ \left[ \dfrac{\sin(\pi a y / \lambda L)}{\pi a y / \lambda L} \right]^2 \cos^2$(\pi d y / \lambda L)$$

Question 9

A circular aperture of diameter $$D$$ produces a diffraction pattern on a distant screen. The angle $$\$$theta_1$$ of the first minimum is given by:

Accepted Answer

$$\sin \$$theta_1$$ = 1.22 \lambda / D$$

Question 10

Which of the following is NOT a practical application of diffraction gratings?

Accepted Answer

Measuring the speed of sound in air

Question 11

In a multi-slit interference pattern, what is the effect of increasing the number of slits $$N$$ while keeping the slit separation $$d$$ and wavelength $$\lambda$$ constant?

Accepted Answer

Principal maxima become narrower and more intense

Question 12

A missing order in a double-slit diffraction pattern occurs when:

Accepted Answer

An interference maximum coincides with a single-slit minimum

Question 13

The central maximum of a single-slit diffraction pattern is much brighter and wider than the secondary maxima. The width $$w of $$the central maximum is given by:

Accepted Answer

$$w = 2 L \lambda / a$$

Question 14

Which statement best describes the difference between the wave and ray models of light in the context of diffraction?

Accepted Answer

The ray model is used when the spreading due to diffraction is less than the size of the opening

Question 15

A Michelson interferometer is used to measure the wavelength of light. If the mirror is moved by $$0.5 \ \mu m$$ and 100 fringes pass by, what is the wavelength of the light?

Accepted Answer

$$\lambda = 2 \Delta L / \Delta m = 2 	imes 0.5 \ \mu m / 100 = 0.01 \ \mu m = 10 \ nm$$

Question 16

Which of the following best describes the principle behind holography?

Accepted Answer

Recording and reconstructing the full wavefront of light scattered from an object using interference

Question 17

In a multi-slit interference pattern, the intensity at an angle $$	heta is $$given by $$I_N(	heta) = I_1$(	heta) \left[ \dfrac{\sin(N \alpha)}{\sin \alpha} ight]^2. $$What does the factor $$\left[ \dfrac{\sin(N \alpha)}{\sin \alpha} ight]^2$$ represent?

Accepted Answer

The N-slit interference factor

Question 18

A laboratory uses a diffraction grating to analyze the spectrum of a star. Why is this technique effective for determining the star's composition?

Accepted Answer

Different elements emit or absorb light at characteristic wavelengths, which are separated by the grating

Wave Optics: Diffraction and Interference

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