Astronomers observe the chromosphere of the Sun with a filter that passes the re

Question

Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the H_alpha line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is held at a constant temperature. Find the minimum value of d that produces maximum transmission of perpendicular H_alpha light if the dielectric has an index of refraction of 1.367. (Assume that the glass's refractive index exceeds 1.367.) If the temperature of the filter increases above the normal value, increases its thickness, what happens to the transmitted wavelength? (Its index of refraction does not change significantly.) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light.

Explanation / Answer

a)  distance down and back to be one whole wavelength in the film

2 t = lambdan = lambda0 / nfilm

t = lambda0 / 2 nfilm = (656.3 * 10-9) / (2 * 1.367) = 240 nm

b) The filter will expand. As t increases wavelength increases

c) lambda0 = nfilm * t = 1.367 * 240 nm

= 328 nm

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