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A prism ABC of angle 30^(@) has its fac...

A prism ABC of angle `30^(@)` has its face AC silvered. A ray of light incident at an angle of `45^(@)` at the face AB retraces its path after refraction at face AB and reflection at face AC . The refractive index of the material of the prism is

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The ray will retrace its path at the silvered face when it is incident normally on it.
So, angle of emergence, e = 0 and therefore, r. = 0
`"As, "r+r.=A" "rArr" "r+0=30^(@)`
`rArr" "r=30^(@)`
Refractive index is
`mu=(sini)/(sinr)=(sin45^(@))/(sin30^(@))=((1)/(sqrt2))/((1)/(2))=sqrt2=1.414`
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