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  4. An isosceles prism of angle A=30° has one of its surfaces silvered. Light rays falling at an angle of incidence 60° on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

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Q. An isosceles prism of angle $A=30^{\circ}$ has one of its surfaces silvered. Light rays falling at an angle of incidence $60^{\circ}$ on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material isPhysics Question Image

Ray Optics and Optical Instruments

Solution:

For light to retrace its path it must reflect normally in the mirror.
When it does so, by geometry $r=30^{\circ}$
$\mu=\frac{\sin i}{\sin r}=\frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\sqrt{3}=1.732$
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