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Chapter 35: Qn 42 (page 1018)

A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle θ2.

Wavelengths for which the index of refraction is n + δn, where δn<<n, are refracted at angle θ2+δθ.

a). Show that the angular separation of the two wavelengths, in radians, is δθ=-(δn/n)tanθ2.

b). A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?

Short Answer

Expert verified

δθ=-(δn/n)tanθ2

δn=-(n/tanθ2)δθ

Step by step solution

01

Given values δn=-0.28οnred=1.552θ1=30ο

a). From Snell's law, we have

sin θ1= n sin θ2and sin θ1

=(n+δn) sin (θ2+δθ)

02

b) we use formula,            δθ=-(δn/n)tanθ2

From previous formula ,we have to find value forδn

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Most popular questions from this chapter

The Hubble Space Telescope has a mirror diameter of 2.4 m. Suppose the telescope is used to photograph stars near the center of our galaxy, 30,000 light years away, using red light with a wavelength of 650 nm.

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A beam of white light enters a transparent material. Wavelengths for which the index of refraction is n are refracted at angle θ2. Wavelengths for which the index of refraction is n+δn, where δn<<n , are refracted at angle θ2+δθ.

a). Show that the angular separation of the two wavelengths, in radians, is δθ=-(δnn)tanθ2

b). A beam of white light is incident on a piece of glass at 30.0°. Deep violet light is refracted 0.28° more than deep red light. The index of refraction for deep red light is known to be 1.552. What is the index of refraction for deep violet light?
See all solutions

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