   Chapter 27, Problem 27PE

Chapter
Section
Textbook Problem

(a) What do the four angles in the above problem become if a 5000-line-per-centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second-order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.

To determine

(a)

What do the four angles in the above problem become if a 5000-line-per-centimeter diffraction grating is used?

Explanation

Given info:

N=5000linescmλ1=409.92nmλ2=433.66nmλ3=486.34nmλ4=656.06nmm=1

Formula used:

There is constructive interference for a diffraction grating when,

dsinθ=mλ,   m=0,1,1,2,2....

Calculation:

First let us find slit separation,

N=5000linescmd=1×1025000=2000nm

λ1=409.92nm

dsinθ=mλθ1=sin1( λ 1d)=sin1(409.922000)=11.80

λ2=433

To determine

(b)

What would the angles be for the second-order maxima using this grating?

To determine

(c)

The relationship between integral reductions in lines per centimeter and the new angles of various order maxima?

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