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    Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm. 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.

    a) Find the minimum value of d that produces the maximum transmission of this perpendicular H light (656.3 nm), if the dielectric has an index of refraction of 1.378.
    b) What happens to the transmitted wavelength if the temperature of the filter is increased but the index of refraction does not change significantly?
    c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorbed this light.

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    Solution Preview

    In order to understand the following, we must be aware of the following points :
    <br>1. The filter will "pass all the light" ( i.e. maximum transmission) for specific wavelengths.
    <br>2. The relation to determine these specific wavelengths must depend on the distance between the plates, the refractive index of the material between the plates and the angle of incidence of the light striking the plate.
    <br>3. Temperature changes can affect either (or both) refractive index or distance between the plates.
    <br>A side note: This filter is sometimes called a Fabry-Perot etalon and used in spectral analysis of a light source.
    <br>Please refer to the attached file for the diagram which ...

    Solution Summary

    Find the thickness of the transparent dielectric.