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Chapter 27: Q33PE (page 998)

At what angle does a diffraction grating produces a second-order maximum for light having a first-order maximum at 20.0掳?

Short Answer

Expert verified

The angle of the second-order maximum is obtained as43.2掳.

Step by step solution

01

Given data

The angle at which the first-order maximum is observed20.0掳

02

Evaluating the angle of the second-order maximum

The equation of the constructive interference can be expressed as

胃蝉颈苍位 鈥︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Where, d, 位, 胃and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

We assume the 胃1is the angle for the first-order maximum (m=1) and 胃2is the angle for the second-order maximum (m=2).

Substituting the given data in equation (1) will give

蝉颈苍胃1=m1位d...........................(2)=位d蝉颈苍胃2=m1位d...........................(3)=2位d

Comparing equations (2) and (3)

sin胃2=2sin胃1胃2=sin鈥�12脳sin20.0掳胃2=43.2掳

Therefore, the angle of the second-order maximum is 43.2掳.

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Most popular questions from this chapter

Calculate the wavelength of light that produces its first minimum at an angle of 36.9掳 when falling on a single slit of width \({\rm{1}}{\rm{.00 \mu m}}\).

At what angle is the first-order maximum for 450-nm wavelength blue light falling on double slits separated by 0.0500 mm?

Suppose a feather appears green but has no green pigment. Explain in terms of diffraction.

(a) If a single slit produces a first minimum at \({\rm{14}}{\rm{.5^\circ }}\),at what angle is the second-order minimum? (b) What is the angle of the third-order minimum? (c) Is there a fourth-order minimum? (d) Use your answers to illustrate how the angular width of the central maximum is about twice the angular width of the next maximum (which is the angle between the first and second minima).

Find the largest wavelength of light falling on double slits separated by 1.20 碌m for which there is a first-order maximum. Is this in the visible part of the spectrum?
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