Question

A light ray incident along vector `2hati+4hatj+sqrt(5)hatk` strikes in the `x-z` from medium of refractive index `sqrt(3)` and enters into medium II of refractive index is `mu_(2)`. The value of `mu_(2)` for which the value of angle of refraction becomes `90^(@)` is
A. `(4sqrt(3))/5`
B. `(3sqrt(3))/5`
C. `(2sqrt(3))/5`
D. `(sqrt(3))/5`

Answer 1

Correct Answer - B
`sintheta_(C)=mu_(2)//mu_(1)`
`1-cos^(2)theta_(C)=((mu_(2))/(mu_(1)))^(2)`
`1-(hatn.hatp)^(2)=((mu_(2))/(mu_(1)))^(2)`
`1-[4/(sqrt(25))]^(2)=((mu_(2))/(mu_(1)))^(2)implies(mu_(2))/(mu_(1))=3/5`
`implies mu_(2)=(3sqrt(3))/5`

Comments

What is n.p ?

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Here, n.p is Projection.