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Let A = angle of prism

i= angle of incident

e = angle of emerging

k=angle of deviation

r1&r2=angle of refraction

u=refractive index of the prism

From quadrilateral APNQ

A+N=180 - (1)

From triangle PNQ

N+r1+r2=180- (2)

From (1)&(2)

A=r1+r2- (3)

By Snell's law

sin i= u sin r1

& u sinr2=sin e

For Snell's angle i.e, r1 & r2

( i = ur1 & e = ur2 ) - (4)

From triangle PQD

k= i-r1+e- r2

= (u-1)r1 + ( u- r2) since [4]

= ( u-1) ( r1- r2)

= k = ( u-1)A since (3)

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