# Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wave-length 656.3 nm, called the H α line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of d that will produce maximum transmission of perpendicular H α light if the dielectric has an index of refraction of 1.378. (b) If the temperature of the filter increases above the normal value increasing its thickness, what happens to the transmitted wavelength? (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

Chapter
Section

### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300
Chapter 24, Problem 23P
Textbook Problem
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## Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wave-length 656.3 nm, called the Hα line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of d that will produce maximum transmission of perpendicular Hα light if the dielectric has an index of refraction of 1.378. (b) If the temperature of the filter increases above the normal value increasing its thickness, what happens to the transmitted wavelength? (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light

(a)

To determine
The minimum value of thickness.

### Explanation of Solution

Given Info: The refractive index is 1.378 , the thickness is 656.3nm , and the order is 1 .

Explanation:

Formula to calculate the thickness is,

d=mλ2nfilm

Here,

λ is the wavelength

m is the order

nfilm is the refractive index of the film

d is the thickness

Substitute 1 for m , 656

(b)

To determine
The change in wavelength with thickness

(c)

To determine
The wavelength of the light reflected completely.

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