1.

There is a prism with refractive index equal to sqrt(2) and the refracting angle equal to 60^(@). One of the refracting surfaces of the prism is polished. A beam of monochromatic light will retrace its path if its angle of incidence over the refracting surface of the prism is

Answer»

`SIN^(-1)(SQRT2)`
`sin^(-1)(2sqrt3)`
`sin^(-1)((sqrt3)/(sqrt2))`
`sin^(-1)((1)/(sqrt2))`

Solution :It is clear from the figure that the RAY will retrace the path when the refracted ray OR is incident normally on the polished surface AC. Thus, angle of refraction `r=60^(@)`.
We know that `mu=(sini)/(SINR)`
`therefore sin i=muxx sin r=sqrt2 xx sin 60^(@)`
`=sqrt2xx(sqrt3)/(2) or i=sin^(-1)sqrt((3)/(2))`


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