Question 130: Ray Optics

Question

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

Accepted Answer

$$n\sin {	heta _c} = 1$$
$$\sin {	heta _c} = {1 \over n}$$
$$i = r$$
$$r' + r + 90^\circ  = 180^\circ $$
$$r' = 90^\circ  - r = 90^\circ  - i$$
$$\cos r' = \cos (90^\circ  - i)$$
$$\cos r' = \sin i$$ ..... (i)
$$n\sin i = \sin r'$$ ..... (ii)
$$n = 	an r'$$
$${1 \over {\sin {	heta _c}}} = 	an r'$$
$$\sin {	heta _c} = \cot r'$$
$$\sin {	heta _c} = 	an r$$
$${	heta _c} = {\sin ^{ - 1}}(	an r)$$

Answer

sin
$$-$$1
(tan r)

Answer

sin
$$-$$1
(cot r)

Answer

sin
$$-$$1
(tan r')

Answer

tan
$$-$$1
(sin i)

Ray Optics

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

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