1.

Light is incident normally on face AB of a prism as shown in Figure. A liquid of refractive index `mu` is placed on face AC of the prism. The prism is made of glass of refractive indes `3//2` . Find the limits of `mu` for which total internal reflection takes place on the face AC.

Answer» Critical angle between glass and liquid face is
`sintheta_(c)=(3//2)/(mu)=(3)/(2mu)`
Angle of incidence at face AC is `60^@` , i.e., `i=60^@` .
For total internal reflection to take place,
`i=theta_(c) or sini gt sintheta_(c)`
or `sin60^@ gt (3)/(2mu)` or ` sqrt((3)/(2)) gt (3)/(2mu)`
or `mu gt sqrt(3)`


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