A,B, and C are the parallel sided transparent media of refractive indices `n_(1),n_(2)` and `n_(3)` respectively. They are arranged as shown in the figure. A ray is incident at an angle `i` on the surface of separation of A and B which is as shown in the figure. After the refraction into the medium B the ray grazes the surfaces of separation of the media B and C. then `sin i` equal to

Options

A. `(n_(3))/(n_(1))`
B. `(n_(1))/(n_(3))`
C. `(n_(2))/(n_(3))`
D. `(n_(1))/(n_(2))`

Answer

A

Explanation

Applying Snel's law between the surfaces A and B

`n_(1)sin i=n_(2)sin r_(1)`………….i
Again applying Snell's law between surfaces B and C
`n_(2) sin r_(1)=n_(3)sin r_(2)`………….ii
From Eqs (i) and (ii) we get
`n_(1)sin i=n_(3)sin r_(2)`
Here `r_(2)=90^(@)`
`:.n_(1)sin i=n_(3)`
`impliessin i=(n_(3))/(n_(1))`