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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°?

Short Answer

Expert verified

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

Step by step solution

01

Given data

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

02

Evaluating the angle of the second-order maximum

The equation of the constructive interference can be expressed as

θsinλ …………………(1)

Where, d, λ, θand 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 θ1is the angle for the first-order maximum (m=1) and θ2is the angle for the second-order maximum (m=2).

Substituting the given data in equation (1) will give

sinθ1=m1λd...........................(2)=λdsinθ2=m1λd...........................(3)=2λd

Comparing equations (2) and (3)

sinθ2=2sinθ1θ2=sin‐12×sin20.0°θ2=43.2°

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

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