Q: A diffraction grating has $$N$$ slits spaced $$d$$ apart. At what angles will bright fringes occur?

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

Q: For single-slit diffraction, at what angles do dark fringes occur?

$$\sin \theta_p = \frac{p \lambda}{a}$$, where $$p = 1, 2, 3, ...$$

Question 1

Which phenomenon explains why water waves spread out after passing through a narrow opening?

Accepted Answer

Diffraction

Question 2

Why does light passing through a large opening produce a sharp-edged shadow, unlike water waves?

Accepted Answer

Light has a very small wavelength compared to the opening

Question 3

In Young’s double-slit experiment, what condition must be met for constructive interference (bright fringes) to occur?

Accepted Answer

$$\Delta r = m \lambda$$, where $$m = 0, 1, 2, 3, ...$$

Question 4

A double-slit experiment uses slits separated by $$d = 0.30 mm $$and a screen $$L = 1.0 m $$away. If ten bright fringes span $$1.7 cm$$, what is the wavelength of the light?

Accepted Answer

$$570 nm$$

Question 5

Which equation gives the intensity of the double-slit interference pattern at position $$y$$?

Accepted Answer

$$I_{double} = 4I_1 \cos^2$ \left( \frac{\pi d y}{\lambda L} \right)$$

Question 6

A diffraction grating has $$N$$ slits spaced $$d$$ apart. At what angles will bright fringes occur?

Accepted Answer

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

Question 7

Light from a sodium lamp passes through a diffraction grating with $$1000$$ slits per mm. Two bright fringes are observed at $$72.88 cm $$and $$73.00 cm $$from the central maximum on a screen $$1.0 m $$away. What are the wavelengths of these fringes?

Accepted Answer

$$589.0 nm $$and $$589.6 nm$$

Question 8

What is the intensity of the bright fringes produced by a diffraction grating with $$N$$ slits?

Accepted Answer

$$I_{max} = N^2$ I_1$

Question 9

A peacock feather appears colorful due to which optical phenomenon?

Accepted Answer

Reflection grating

Question 10

For single-slit diffraction, at what angles do dark fringes occur?

Accepted Answer

$$\sin 	heta_p = \frac{p \lambda}{a}$$, where $$p = 1, 2, 3, ...$$

Question 11

A helium-neon laser ($$\lambda = 633 nm) $$passes through a slit and the first minimum is $$1.2 cm $$from the central maximum on a screen $$2.0 m $$away. What is the width of the slit?

Accepted Answer

$$0.11 mm$$

Question 12

How does the width of the central maximum in a single-slit diffraction pattern change if the slit width $$a$$ decreases?

Accepted Answer

The central maximum becomes wider

Question 13

For a circular aperture, what is the angle of the first minimum in the diffraction pattern?

Accepted Answer

$$\$$theta_1$$ = 1.22 \frac{\lambda}{D}$$

Question 14

A Michelson interferometer produces a new maximum each time the mirror moves by what distance?

Accepted Answer

$$\lambda / 2$$

Question 15

An experimenter moves the mirror in a Michelson interferometer by $$3.164 mm $$and observes $$10,000$$ new bright spots. What is the wavelength of the light?

Accepted Answer

$$632.8 nm$$

Question 16

Which model of light is most appropriate when light passes through an opening smaller than $$1 mm$$?

Accepted Answer

Wave model

Question 17

What principle states that each point on a wave front acts as a source of spherical wavelets?

Accepted Answer

Huygens’ principle

Question 18

Which device uses interference to make very precise measurements by dividing and recombining a single wave?

Accepted Answer

Interferometer

Question 19

If an interference maximum falls exactly on a minimum in the single-slit diffraction pattern, what is observed?

Accepted Answer

A missing order

Question 20

Which optical phenomenon allows holography to reconstruct a three-dimensional image?

Accepted Answer

Diffraction and interference

Wave Optics: Diffraction and Interference of Light

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