The refractive index of transparent cylindrical rod is `(2)/(root_3)` . As shown in the figure the ray i incident at the mid point of its one end. For which angle of incidence, the ray become parallel to the length of rod ?

Options

A. `sin^-1((1)/(root_3))`
B. `sin^-1((1)/(2))`
C. `sin^-1((root_3)/(2))`
D. `sin^-1((2)/(root_3))`

Answer

A, C

Explanation

According to Snell.s law `n = (sin theta)/(sin alpha)`
` therefore(2)/(sqrt3)=(sintheta)/(sin alpha)`….....(1)
Now, from Snell.s law,
In `n_2sin theta_2=n_1sin theta_1,n_2/n_1sin theta_2=sintheta_1`
`nsin beta=sin90^@`
`therefore" "n sin beta=1`
`sin beta=1/n=(sqrt3)/(2)`
`therefore beta=60^@`
`thereforealpha=90^@-beta=90^@-60^@=30^@`
`therefore` By substituting value of a in equation (1),
`(2)/(sqrt3)=(sintheta)/(sin30^@)`
`sin theta=(2)/(sqrt3)xx1/2`
`sin theta=(1)/(sqrt3)`
`thereforetheta=sin^(-1)((1)/(sqrt3))`