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What should be the minimum value of refractive indexof a prism of refractive angle A, so that there is no emergent ray irrespective of angle of incidence? |
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Answer» sin`A/2` From Snell.s law at face AB, we have 1sini=nsin`r_1`…(II) `A=r_1+r_2=r_1+C`…(iii) From eqn. (ii) N is minimum when `r_1` is maximum , i.e., `r_1=C`. In this CASE `i=90^@` From eqn. (iii) , A=2C or C=A/2 From eqn. (ii), sin C=`1/n`, sin`A/2=1/n` `therefore` n=cosec`A/2` 
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