Q: Which equation gives the angular position of the first minimum in a single-slit diffraction pattern?

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

Question 1

Which experiment provided the first strong evidence for the wave nature of light by demonstrating an interference pattern?

Accepted Answer

Young's double-slit experiment

Question 2

In Young’s double-slit experiment, what is the condition for constructive interference at a point on the screen?

Accepted Answer

The path difference equals an integer multiple of the wavelength: $$d \sin 	heta = m \lambda$$

Question 3

A diffraction grating is used to analyze the light from a distant star. What is the main advantage of using a grating with a large number of slits?

Accepted Answer

It produces sharper and brighter maxima, allowing for more precise wavelength measurements.

Question 4

Which of the following best describes Huygens’ Principle?

Accepted Answer

Each point on a wavefront acts as a source of new wavelets that spread out in all directions.

Question 5

When white light passes through a diffraction grating, what is observed on the screen?

Accepted Answer

A continuous spectrum of colors, with each color appearing at a different angle

Question 6

In a single-slit diffraction experiment, what happens to the width of the central maximum if the slit width is decreased?

Accepted Answer

The central maximum becomes wider.

Question 7

Which equation gives the angular position of the first minimum in a single-slit diffraction pattern?

Accepted Answer

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

Question 8

A soap bubble shows colorful patterns when illuminated by white light. What physical phenomenon is responsible for this?

Accepted Answer

Thin-film interference

Question 9

Why does violet light bend more than red light when passing through a prism?

Accepted Answer

The index of refraction is higher for violet light due to its shorter wavelength.

Question 10

In the Michelson interferometer, what happens when the path length difference between the two arms is an integer multiple of the wavelength?

Accepted Answer

Constructive interference occurs, producing a bright fringe.

Question 11

A student observes that the maxima in a double-slit experiment become closer together when the screen is moved farther away. Which equation explains this observation?

Accepted Answer

$$y_m = \frac{m \lambda L}{d}$$

Question 12

Which of the following is a real-world application of diffraction gratings?

Accepted Answer

Spectroscopy for identifying elements by their spectral lines

Question 13

What is the main reason that the maxima in a diffraction grating pattern are much sharper than those in a double-slit pattern?

Accepted Answer

There are many more slits, causing more constructive and destructive interference.

Question 14

Which phenomenon was crucial in the first direct detection of gravitational waves by LIGO?

Accepted Answer

Interference of light in a Michelson interferometer

Question 15

If the thickness of a thin film is exactly one-quarter of the wavelength of incident light, what type of interference will occur for the reflected light (assuming a $$\pi$$ phase shift upon reflection at the top surface)?

Accepted Answer

Destructive interference

Question 16

Which of the following best explains why the central maximum in a single-slit diffraction pattern is brighter and wider than the other maxima?

Accepted Answer

It is due to the constructive interference of all wavelets from the slit arriving in phase at the center.

Question 17

Which law is used to determine the change in wavelength of light as it enters a new medium?

Accepted Answer

Snell’s Law: $$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2$$

Question 18

A scientist uses a Michelson interferometer to measure the wavelength of a laser. If the movable mirror is shifted by $$0.5 \lambda$$, how many bright fringes will move past a reference point?

Accepted Answer

One

Question 19

Which of the following statements about dispersion is correct?

Accepted Answer

Red light is refracted less than blue light because it has a longer wavelength.

Question 20

In the context of wave optics, what is the main difference between interference and diffraction?

Accepted Answer

Interference is the result of the superposition of waves from two or more sources, while diffraction is the spreading of waves when they encounter an obstacle or slit.

The Wave Nature of Light: Interference, Diffraction, and Applications

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