1.

Angle of a prism 30^(@) and its refractive index is sqrt2 and one of the prism surface is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path

Answer»

`30^(@)`
`60^(@)`
`45^(@)`
`sin^(-1)sqrt(1.5)`

Solution :Here `angleA=30^(@) and n = sqrt2`. Since light ray retraces its PATH when
incident on the silvered surface, hence `angler_(2)=0^(@)`.
`because angler_(1)+angler_(2)=angleA" hence "r_(1)=A=30^(@)`
As `(sini)/(sinr_(1))=n RARR sini = n sin r_(1)=sqrt2xx sin 30^(@)=sqrt2xx(1)/(2)=(1)/(sqrt2)`
`rArr""i=sin^(-1)((1)/(sqrt2))=45^(@)`


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