JEE MAIN - Physics (2021 - 22th July Evening Shift - No. 13)
A ray of light passes from a denser medium to a rarer medium at an angle of incidence i. The reflected and refracted rays make an angle of 90$$^\circ$$ with each other. The angle of reflection and refraction are respectively r and r'. The critical angle is given by
_22th_July_Evening_Shift_en_13_1.png)
sin$$-$$1 (tan r)
sin$$-$$1 (cot r)
sin$$-$$1 (tan r')
tan$$-$$1 (sin i)
Explanation
_22th_July_Evening_Shift_en_13_2.png)
$$n\sin {\theta _c} = 1$$
$$\sin {\theta _c} = {1 \over n}$$
$$i = r$$
$$r' + r + 90^\circ = 180^\circ $$
$$r' = 90^\circ - r = 90^\circ - i$$
$$\cos r' = \cos (90^\circ - i)$$
$$\cos r' = \sin i$$ ..... (i)
$$n\sin i = \sin r'$$ ..... (ii)
$$n = \tan r'$$
$${1 \over {\sin {\theta _c}}} = \tan r'$$
$$\sin {\theta _c} = \cot r'$$
$$\sin {\theta _c} = \tan r$$
$${\theta _c} = {\sin ^{ - 1}}(\tan r)$$
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