Two media are separated by a plane surface. Speed of light in one medium is $2.0 imes 10^{8} \math

Question

Two media are separated by a plane surface. Speed of light in one medium is $2.0 	imes 10^{8} \mathrm{~m} / \mathrm{s}$ and that in another medium is $2.4 	imes 10^{8} \mathrm{~m} / \mathrm{s}$. Deduce the critical angle for a ray going from the first medium into the second.\

Professor PC Thomas Classes · Answer

Speed of light in first medium is\ $2 	imes 10^{8} \mathrm{~m} / \mathrm{s}$. speed of light in second medium is $2.4 	imes 10^{8} \mathrm{~m} / \mathrm{s}$. So the first medium is the denser medium and second medium is the rarer medium. For critical angle, the ray must travel from denser to rarer medium. $\mathrm{n}=\frac{1}{\sin \mathrm{c}}$ where $\mathrm{n}=$ refractive index of denser medium, c is the critical angle in the denser medium. Refractive index of the denser medium\ $=\frac{	ext { speed of light in rarer medium }}{	ext { speed of light in deser medium }}$\ $=\frac{2.4 	imes 10^{8}}{2 	imes 10^{8}}=\frac{6}{5}$\ $\sin c=\frac{1}{n}=\frac{5}{6}$\ $c=\sin ^{-1}\left(\frac{5}{6}ight)$\