   Chapter 27, Problem 42PE

Chapter
Section
Textbook Problem

Construct Your Own ProblemConsider a spectrometer based on a diffraction grating. Construct a problem in which you calculate the distance between two wavelengths of electromagnetic radiation in your spectrometer. Among the things to be considered are the wavelengths you wish to be able to distinguish, the number of lines per meter on the diffraction grating, and the distance from the grating to the screen or detector. Discuss the practicality of the device in terms of being able to discern between wavelengths of interest.

To determine

The construction of a problem in which the distance between two wavelengths of electromagnetic radiation in spectrometer is calculated.

Explanation

Formula used:

The equation for diffraction grating is given as,

dsinθ=nλ

Calculation:

The distance between first order maxima for two wavelengths can be calculated if the angle of maxima is known.

Consider a grating having 10000 lines per centimeter.

The distance between the two slits is,

d=1cm10000d=1.0×106m

When a light of wavelength 400nm is incident on diffraction grating, the angle of first order maxima is,

sinθ1=nλ1dsinθ1=1×400× 10 91.0× 10 6θ1=sin1(0.4)θ1=23.58°

When a light of wavelength 750nm is incident on diffraction grating, the angle of first order maxima is,

sinθ2=nλ2dsinθ2=1×750× 10 91

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