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A ray of light incident on the horizonta...

A ray of light incident on the horizontal surface of a glass slab at `70^@` just grazes the adjacent vertical surface after refraction. Complete the critical angle and refractive index of glass.

Text Solution

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From Fig. for total internal reflection at `B`.
`r + C = 90^(@), r = 90^(@) - C`
According to Snell's law, `mu = (sin i)/(sin r) = (sin 70^(@))/(sin(90^(@) - C)) = (sin 70^(@))/(cos C)`
Also, `mu = (1)/(sin C)`
`:. (sin 70^(@))/(cos C) = (1)/(sin C)` or `(sin C)/(cos C) = (1)/(sin 70^(@))`
`tan C = (1)/(0.9397) = 1.0642 :. C = tan^(-1)(1.0642) = 46^(@)47'`
Also `mu = (1)/(sin C) = (1)/(sin 46^(@)47') = (1)/(0.7288) = 1.372`
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