First slide

Ray optics

Question

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

Moderate

A

sin^–1(tan r)
B

tan^–1(sin r)
C

sin^–1(tan r¹)
D

tan^–1(sin r¹)

Solution

i = r ; r + r¹ - 90 ; r¹ = 90 - r
$(μ_{r}) \sin r^{1} = (μ_{d}) \sin i \Rightarrow cosr = \frac{1}{\sin θ_{c}} \sin r since [\frac{μ_{d}}{μ_{r}} = \frac{1}{\sin θ_{c}}] \Rightarrow θ_{c} = \sin^{- 1} (\tan r)$

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