Question

When a light ray is refracted from one medium into another the wavelength change from $4500A^0$ to $3000A^0$ the critial angle for a ray from second medium to first medium is

• A. ${sin}^{-1}\left(\frac{2}{3}\right)$
• B. ${cos}^{-1}\left(\frac{2}{3}\right)$
• C. ${tan}^{-1}\left(\frac{3}{2}\right)$
• D. ${tan}^{-1}\left(\frac{2}{\sqrt{5}}\right)$

Answer 1

The correct option is A ${sin}^{-1}\left(\frac{2}{3}\right)$

${\lambda }_1=4500A^{\circ }$

${\lambda }_2=3000A^{\circ }$

Refractive index of second medium w.r.t first medium = $\frac{{\mu }_2}{{\mu }_1}$

Refractive index is inversely proportional to wave length. i.e.

$\frac{{\mu }_2}{{\mu }_1}=\frac{{\lambda }_1}{{\lambda }_2}=\frac{4500}{3000}=\frac{3}{2}$

${}_2{\mu }_1=\frac{3}{2}$

Critical angle is given by the formula

$\sin C=\frac{1}{{}_2{\mu }_1}$

$\sin C=\frac{1}{\frac{3}{2}}$

$\sin C=\frac{2}{3}$

$C={\sin }^{-1}\left(\frac{2}{3}\right)$