Consider an equilateral prism ABC as shown in the figure. A ray of light is incident on the face AB and gets transmitted through the prism. Then total internal reflection takes place at the face BC and the ray comes out of prism through the face AC. The total angle of deviation is `120^(@)`. Minimum value of refractive index m of the material of the prism should be

Options

A. `sqrt(4/5)`
B. `sqrt(5/3)`
C. `sqrt(2)`
D. `sqrt(7/3)`

Answer

D

Explanation

`30 + x + 60 + x = 180^(@)`
`(90-r)`
`i - r + i - r +60 + 2r = 120`
`2i = 60^(@)`
`i = 30^(@)`
`1/2 - 4 sin r`
`sin r = 1/(2u)`
`sin (60-r) ge 1/u`
`(sqrt(3))/(2) cos r - 1/2 sin r u . 1/u`
`(sqrt(3))/(2) xx (sqrt(4u^(2)-1))/(2u) - 1/2 xx 1/(2u) ge 1/u`
`sqrt(3) (4u^(2) - 1)^(1//2) ge 5`
`3(4u^(2)-1) ge 25`
`12u^(2) - 3 ge 25`
`u^(2) ge 28/12`
`u ge sqrt(7/3)`.