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Chapter 27: Q24PE (page 997)

What is the distance between lines on a diffraction grating that produces a second-order maximum for760鈥�nmred light at an angle of60.0鈭�?

Short Answer

Expert verified

The distance between the lines on the diffraction grating is \({\bf{1}}{\bf{.76 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{ m}}\).

Step by step solution

01

Given data

The wavelength of the red light is位=760nm10鈥�9m10nm=7.60'10鈥�7m

The order of maximum is 2.

The angle at which the first-order maximum is observed60.0鈭�

02

Evaluating the lines per second-order maximum

The equation of the constructive interference can be expressed as

d蝉颈苍胃=尘位鈥︹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.

Therefore, if we substitute the given data in equation (1) for m=2, we will get,

d=2位蝉颈苍胃=2脳7.60脳10鈥�7msin60.0鈭�=1.76脳10鈥�6m

Therefore, the line for the second-order maximum is \({\bf{1}}{\bf{.76 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{ m}}\)

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