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Chapter 33: Q. 10 (page 955)

Light of wavelength620nmilluminates a diffraction grating. The second-order maximum is at angle 39.5掳. How many lines per millimeter does this grating have?

Short Answer

Expert verified

There aren=512lines per millimeter does this grating have

Step by step solution

01

Step1:  definition of light of wavelength

As a result, the wavelength is defined as the distance between the crest or trough of one wave and the crest or trough of the next wave. The wavelength of light is defined as "the distance between the light wave's two successive crests or troughs."

02

Find how many lines per meter

In order to obtain constructive interference from a diffraction grating, the following conditions must be met.

dsin鈦�胃m=m位

m=0,1,2,3,鈥�

We can use the previous equation to calculate the distance between any two successive slits d if we know the angle of the second-order maximum and the wavelength used to illuminate the grating.

d=2位sin鈦�胃2=2脳620脳10鈭�9msin鈦�39.5鈭�=1.95脳10鈭�6m

The number of lines per millimetre can now be calculated as

n=1mmd=1脳10鈭�3m1.95脳10鈭�6m=512

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Most popular questions from this chapter

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 (位=1.000渭m)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鈥檚 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.

b. What is the first index of refraction of the electro-optic crystal larger than 1.522that changes the optical switch to the state opposite the state you found in part a?

The intensity at the central maximum of a double-slit interference pattern is 4I1. The intensity at the first minimum is zero. At what fraction of the distance from the central maximum to the first minimum is the intensity I1? Assume an ideal double slit.

Light of wavelength550nm illuminates a double slit, and the interference pattern is observed on a screen. At the position of the m=2 bright fringe, how much farther is it to the more distant slit than to the nearer slit?

It shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if the

a. The wavelength of the light is increased.

b. The diameter of the aperture is increased.

c. How will the screen appear if the aperture diameter is less than the light wavelength?

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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