The maximum value of index of refraction of a material of a prism which allows the passage of light through it when the refracting angle of prism is A is

Options

A. `sqrt(1+si nA/2)`
B. `sqrt(1+ta n^2A/2)`
C. `sqrt(1+ta n^2A/2)`
D. `sqrt(1+co t^2 A/2)`

Answer

D

Explanation

If light comes out of prism for this, no T.I.R. at the emergent face AC i.e.
`r^'leC`
`(r+r^'=A)`
`(A-r)leC`
`Ale(r+C)`
`r_(max)=C` if `i=90^@`
`Ale2C`
`A/2leCimpliesA/2lesin^-1(1/mu)`
`1/mugesin(A/2)`
`mulecosec(A/2)`
`mulesqrt(1+cot^2(A/2))`
`mu_(max)=sqrt(1=cot^2(A/2))`