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What should be the minimum value of refr...

What should be the minimum value of refractive index of a prism of refractive angle A, so that there is no emergent ray irrespective of angle of incidence?

A

sin`A/2`

B

cos`A/2`

C

cosec`A/2`

D

sec`A/2`

Text Solution

Verified by Experts

The correct Answer is:
C
If the ray just emerges from face AC, `e=90^@` and `r_2=C` ….(i)
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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Knowledge Check

  • A ray of light is incident on a refracting face of glass prism of refracting angle 30^@ . If the ray emerges normally from the second refracting surface, the angle of incidence is refracting surface, the angle of incidence is [""_(a)mu_(g) = 1.5]

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