Q20 of 26 Page 1

A. A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of 30o. Calculate the speed of light through the prism.


B. Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.

Given: -


Minimum deviation, = 30o


Prism is equilateral



Formula: -


The Refractive index of the prism in terms of minimum deviation is found as,



Where, is called the minimum deviation, and A is called the angle of the prism.


Calculation: -





Hence,



Also, we know that,




So,




Conclusion: -


the velocity of light in the given prism is, 2.12 × 108 m/s.


B) For emerging ray to graze along face AC,



TIR must occur on the face AC, so,



Hence, rAC = 45o


Also, in quadrilateral AQNR,



As, Q = R = 90o,


A + N = 180o


As, A = 60o , N = 180o – 60o = 1200


Also,




Applying Snell’s law on face AB,





Hence for grazing incidence on face AC,


SiniAB=√2× sin(15o) =1.414× 0.2588=0.366


SiniAB=0.366


iAB=21o (approx.)


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