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Chapter 33: Q. 51 (page 957)

Light from a sodium lamp λ=589nmilluminates a narrow slit and is observed on a screen 75cmbehind the slit. The distance between the first and third dark fringes is 7.5mm. What is the width (in mm) of the slit?

Short Answer

Expert verified

The slit's width of is 0.12mm.

Step by step solution

01

Step: 1 Width of slit:

The light casts a shadow when the slit widths are bigger than the wavelength of the sunshine. Light diffraction occurs when the slit widths are small, and also the light waves overlap on the screen. As a result, the sunshine intensity rises because the slit width grows.

02

Step: 2 Equating part:

In one slit, the location of pth darkest fringes is

yp=pλLa

Calculating the difference by

Δyp=ΔpλLa.

03

Step: 3 Slit's width value:

The width of slit by

a=ΔpλLΔypa=(3−1)×5.89×10−7×0.757.5×10−3a=1.178×10−4ma=0.12mm.

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Most popular questions from this chapter

For what slit-width-to-wavelength ratio does the first minimum of a single-slit diffraction pattern appear at (a) 30°, (b) 60°, and (c) 90°?

A Michelson interferometer using 800nm light is adjusted to have a bright central spot. One mirror is then moved 200nm forward, the other 200nm back. Afterward, is the central spot bright, dark, or in between? Explain.

FIGURE P33.56shows the light intensity on a screen behind a single slit. The wavelength of the light is600nmand the slit width is 0.15mm. What is the distance from the slit to the screen?

To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing d. The small-angle approximation is usually not valid for diffraction gratings, because dis only slightly larger than λ, but assume that the λ/dratio of this grating is small enough to make the small-angle approximation valid.

a. Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance Lbehind the grating.

b. Rather than a screen, suppose you place a piece of film at distance L behind the grating. The bright fringes will expose the film, but the dark spaces in between will leave the film unexposed. After being developed, the film will be a series of alternating light and dark stripes. What if you were to now “play” the film by using it as a diffraction grating? In other words, what happens if you shine the same laser through the film and look at the film’s diffraction pattern on a screen at the same distance L? Demonstrate that the film’s diffraction pattern is a reproduction of the original diffraction grating

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is 600nmand the slit width is 0.15mm. What is the distance from the slit to the screen?
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