4.1 Single-Slit Diffraction

Waves spreading past an opening comparable to their wavelength, and the destructive-interference condition that fixes the dark minima on the screen.

University Physics Volume 3, 4.1 Single-Slit Diffraction

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11 exercises

4.1 Exercise 1

Suppose the slit width in the example is increased to $1.8 \times 10^{−6} \text{m} .$ What are the new angular positions for the first, second, and third minima? Would a fourth minimum exist?

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4.1 Exercise 2

As the width of the slit producing a single-slit diffraction pattern is reduced, how will the diffraction pattern produced change?

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4.1 Exercise 4

If you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. Explain.

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4.1 Exercise 6

In our study of diffraction by a single slit, we assume that the length of the slit is much larger than the width. What happens to the diffraction pattern if these two dimensions were comparable?

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4.1 Exercise 8

(a) At what angle is the first minimum for 550-nm light falling on a single slit of width $1.00 \mu \text{m}$ ? (b) Will there be a second minimum?

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4.1 Exercise 10

(a) How wide is a single slit that produces its first minimum for 633-nm light at an angle of $28.0 °$ ? (b) At what angle will the second minimum be?

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4.1 Exercise 12

Find the wavelength of light that has its third minimum at an angle of $48.6 °$ when it falls on a single slit of width $3.00 \mu \text{m}$ .

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4.1 Exercise 14

Consider a single-slit diffraction pattern for $\lambda = 589 \text{nm}$ , projected on a screen that is 1.00 m from a slit of width 0.25 mm. How far from the center of the pattern are the centers of the first and second dark fringes?

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4.1 Exercise 16

(a) What is the minimum width of a single slit (in multiples of $\lambda$ ) that will produce a first minimum for a wavelength $\lambda$ ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?

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4.1 Exercise 18

If the separation between the first and the second minima of a single-slit diffraction pattern is 6.0 mm, what is the distance between the screen and the slit? The light wavelength is 500 nm and the slit width is 0.16 mm.

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4.1 Exercise 20

An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 600-Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.800 m wide and the speed of sound is 340 m/s?

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