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A crystalline plate cut parallel to its ...

A crystalline plate cut parallel to its optical axis is `0.25mm` thick and serves as a quarter-wave plate for a wavelength`lambda = 530nm`. At what other wavelength of visible spectrum will it also serve as a quarter-wave plate? The difference of refractive indices for extraordinary and ordianry rays is assumed to the constant and equal to `n_(e) - n_(0) = 0.0090` at all wavelength of the visible spectrum.

Text Solution

Verified by Experts

Here
`delta = (2pi)/(lambda) xx 0.009 xx 0.25m`
`= (4.5 pi)/(lambda) , lambda "in" mu m`
We check that for `lambda = 428.6 nm delta = 10.5 pi`
`lambda = 529.4 nm delta = 8.5 pi`
`lambda = 692.3 nm delta = 6.5 pi`
These are the only values of `lambda` for which the plate acts as a quarter wave plate.
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Knowledge Check

  • A light wave of wavelength lambda_(0) propagates from point A to point B. We introduce in its path a glass plate of refractive index n and thickness l. Then introduction of the plate alters the phase of the plate at B by an angle phi . If lambda is the wavelength of light on emeriging from the plate, then

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