Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence.

Options

A. n `gt sqrt(2)`
B. n = 1
C. n= 1.1
D. n= 1.3

Answer

A

Explanation

Since, r + `i = 90^(@) rArr i= 90 - r `for TIR
`i gt i_(c ) ` (Critical angle ) `" " rArr sini gt sini_(c ) `
`rArr " " sin(90^(@) -r) gt sini_(c ) rArr " " cos r gt sin i_(c)`
`rArr " " sqrt(1 - sin^(2) r ) gt (1)/(n)`
Now, sin `alpha = n `sin r
`rArr sin r = (sin alpha)/(n) `
`rArr 1 - (sin^(2) alpha)/(n^(2)) gt (1)/(n^(2)) rArr n^(2) - sin^(2) alpha gt 1 `
`rArr " " n^(2) gt 1 + sin^(2) alpha " " because sin alpha = 1 `
`rArr " " n^(2) gt 2 rArr n gt sqrt(2).`