   Chapter 27, Problem 51PE

Chapter
Section
Textbook Problem

(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 μm .(b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.

To determine

(a)

The angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00µm?

Explanation

Given info:

λ1=589.1nmλ2=589.6nmD=2μm=2000nmm=1

Formula used:

There is destructive interference for a single slit when,

Dsinθ=mλ,   m=1,1,2,2....

Calculation:

We have,

Dsinθ1=mλ12000×sinθ1=1×589

To determine

(b)

What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit?

To determine

(c)

The ease or difficulty of measuring such a distance?

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