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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°. 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⁡θm=mλ

m=0,1,2,3,…

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=2λsin⁡θ2=2×620×10−9msin⁡39.5∘=1.95×10−6m

The number of lines per millimetre can now be calculated as

n=1mmd=1×10−3m1.95×10−6m=512

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Most popular questions from this chapter

Your artist friend is designing an exhibit inspired by circular-aperture diffraction. A pinhole in a red zone is going to be illuminated with a red laser beam of wavelength 670nm, while a pinhole in a violet zone is going to be illuminated with a violet laser beam of wavelength 410nm. She wants all the diffraction patterns seen on a distant screen to have the same size. For this to work, what must be the ratio of the red pinhole’s diameter to that of the violet pinhole?

FIGUREP33.36shows the light intensity on a screen behind a double slit. The slit spacing is 0.20mmand the screen is 2.0mbehind the slits. What is the wavelength (in nm) of the light?

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1cmacross, and you estimate that the distance from the window shade to the wall is about 3m.. Estimate (a) the average wavelength of the sunlight (in nm ) and (b) the diameter of the pinhole (in mm ).

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?

A diffraction grating produces a first-order maximum at an angle of 20.0°. What is the angle of the second-order maximum?
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