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A narrow beam of monochromatic light, pe...

A narrow beam of monochromatic light, pe, is incident normally on one face of an equiangular glass prism of refractive inder 1-45. When the prism is immersed in a certain liquid, the ray makes a grazing emergence along the other face (See below figure). Find the refractive index of this liquid.

Text Solution

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`""_(l)mu_(g)=(1)/(sin C)`
`angleA=60^(@)`
`angleA+angleARP=90^(@)`
So, `angleARP=90^(@)`
So, `angleC=60^(@)`
`""_(l)mu_(g)=(1)/(sin 60^(@))=(2)/( sqrt(3))`
`""_(g)mul= sqrt(3//2)=0*866`
`_(g)mu_(l)=""_(a)mu_(g)xx""_(g)mu_(l)`
`=1*45xxmu_(g)mu_(l)`
`=1*256`
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