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Question

Physics Question on Refraction of Light

Relation between critical angle of water and the glass is

A

Cw=Cg=0C_{ w }=C_{ g }=0

B

Cw=CgC_{ w }=C_{ g }

C

Cw>CgC_{ w }>C_{ g }

D

Cw<CgC_{ w } < C_{ g }

Answer

Cw>CgC_{ w }>C_{ g }

Explanation

Solution

We know that the critical angle for water and glass are given by, sin⁡Cw=1μw⇒Cwsin⁡−1(1μw)\sin C_{ w }=\frac{1}{\mu_{w}} \Rightarrow C_{w} \sin ^{-1}\left(\frac{1}{\mu_{w}}\right) sin⁡Cg=1μx⇒Cgsin⁡−1(1μR)\sin C_{ g }=\frac{1}{\mu_{x}} \Rightarrow C_{g} \sin ^{-1}\left(\frac{1}{\mu_{R}}\right) since     μw1μs\,\,\,\,\mu_{w}\frac{1}{\mu_{s}} ⇒    sin⁡−1(1μw)>sin⁡−1(1μs)\Rightarrow \,\,\,\,\sin ^{-1}\left(\frac{1}{\mu_{w}}\right)>\sin ^{-1}\left(\frac{1}{\mu_{s}}\right) ∴     Cw>Cg\therefore \,\,\,\,\,C_{w}>C_{g}