Question

When a ray is refracted from one medium to another, the wavelength changes from $600\stackrel{\circ }{A}to400\stackrel{\circ }{A}$. The critical angle for the interface will be

• A. $co{s}^{-1}\left(\frac{2}{3}\right)$
• B. $si{n}^{-1}\left(\frac{2}{\sqrt{3}}\right)$
• C. $si{n}^{-1}\left(\frac{2}{3}\right)$
• D. $co{s}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Answer 1

The correct option is C $si{n}^{-1}\left(\frac{2}{3}\right)$

${}_u{\mu }_2=\frac{1}{sinC}\Rightarrow \frac{{\mu }_2}{{\mu }_1}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{1}{sinC}\Rightarrow \frac{6000}{4000}=\frac{1}{sinC}\Rightarrow C=si{n}^{-1}\left(\frac{2}{3}\right)$