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Chapter 27: Q21PE (page 997)

A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520nm -wavelength green light?

Short Answer

Expert verified

The first order maximum is obtained as 5.970.

Step by step solution

01

Given data

Grating lines on the diffraction grating are 2000 liner per cm, which means that the distance between the two slits isd=1cm20001m100cm=5.0脳10-6m

The wavelength of the green light is位=520nm10-9m1nm=5.20脳10-7m

The order of maximum is 1.

02

Evaluating the first-order maximum

In order to calculate the angle, we are supposed to firstly find the distance between slits in the grating, for the value of d, and then solve the equation of the constructive interference,

d蝉颈苍胃=尘位

The value here is for 胃when m=1.

胃=sin-1位d=sin-15.2脳10-7m5.0脳10-6m=sin-1(0.104)=5.970

Therefore, the first-order maximum is 5.970.

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