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If one face of a prism angle 30^(@) "and...

If one face of a prism angle `30^(@) "and" mu= sqrt2` is silvered , the incident ray retraces its initial path. What is the angle of incidence?

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As incident ray retraces its path the ray is incident normally on the silvere face of the prism as shown in figure.

Further , as in `DeltaAED 30^(@) + 90^(@) + angleD= 180^(@) implies angleD = 60^(@)`
Now as by construction , `angleD + angler = 90^(@) implies angler = 90^(@) - 60^(@) = 30^(@)`
`therefore` from Snell's law at surface `AC`, `1 "sin"i sqrt(2)"sin"30^(@)= sqrt(2) xx (1)/(2) = (1)/(sqrt(2)) therefore "sin"i = (1)/(sqrt(2)) implies i = 45^(@)`
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