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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

FIGURE shows the light intensity on a screen 2.5mbehind an aperture. The aperture is illuminated with light of wavelength 620nm.

a. Is the aperture a single slit or a double slit? Explain.

b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

A helium-neon laser (λ=633nm)illuminates a single slit and is observed on a screen1.5mbehind the slit. The distance between the first and second minima in the diffraction pattern is 4.75mm. What is the width (inmm)of the slit?

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Optical computers require microscopic optical switches to turn signals on and off. One device for doing so, which can be implemented in an integrated circuit, is the Mach-Zender interferometer seen in FIGURE. Light from an on-chip infrared laser (λ=1.000μm)is split into two waves that travel equal distances around the arms of the interferometer. One arm passes through an electro-optic crystal, a transparent material that can change its index of refraction in response to an applied voltage. Suppose both arms are exactly the same length and the crystal’s index of refraction with no applied voltage is1.522.

a. With no voltage applied, is the output bright (switch closed, optical signal passing through) or dark (switch open, no signal)? Explain.

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FIGURE Q33.1 shows light waves passing through two closely spaced, narrow slits. The graph shows the intensity of light on a screen behind the slits. Reproduce these graph axes, including the zero and the tick marks locating the double-slit fringes, then draw a graph to show how the light-intensity pattern will appear if the right slit is blocked, allowing light to go through only the left slit. Explain your reasoning.
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