A ray of light from a denser medium strikes a rarer a medium. The reflected and refracted rays make an angle of $90^{o}$ with each other. The angles of reflection and refraction are $r$ and $r^{1} .$ The critical angle would be

see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*

An Intiative by Sri Chaitanya

$s i n^{- 1} (t a n r)$

$t a n^{- 1} (s i n r)$

$t a n^{- 1} (s i n r^{1})$

$s i n^{- 1} (t a n r^{1})$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} r + r^{1} = 90^{o} \Rightarrow r^{1} = 90 - r, i = r \\ μ_{D} \sin i = μ_{r} \sin r^{1} \\ μ (\sin r) = (1) \sin (90 - r) \\ μ \sin r = \cos r \\ t a n r = \frac{1}{μ} \\ \sin c = \frac{1}{μ} \\ c = \sin^{- 1} (\tan r) \end{array}$