Let the refractive index of a denser medium with respect to a rarer medium be `n_(12)` and its critical angle be `theta_(c)`. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is `90^(@)`, Angle A given by -

Options

A. `(1)/(tan^(-1)(sin theta_(C )))`
B. `(1)/(tan^(-1)(sin theta_(C)))`
C. `cos^(-1)(sin theta_(C))`
D. `tan^(-1)(sin theta_(C))`

Answer

D

Explanation

From Snell.s law, `(mu_(R ))/(mu_(D ))=(sini)/(sinr)" ….(i)"`

`because anglei=A and angler=(90^(@)-A)`
We also know that, `sin theta_(C )=(mu_(R ))/(mu_(D ))`
From `eq^(n)(i)," "sin theta_(C )=(sin A)/(sin(90^(@)-A))`
`sin theta_(C )=(sinA)/(cosA)`
`sin theta_(C )=tanA or A=tan^(-1)(sin theta_(C ))`