Question

The refractive indices of the crown glass for blue and red light are 1.51 and 1.49 respectively and those of the flint glass are 1.77 and 1.73 respectively. An isosceles prism of angle $6^o$ is made of crown glass. A beam of white light is incident at a small angle on this prism. The other flint glass isosceles prism is combined with the crown glass prism such that there is no deviation of the incident light.The angle of the flint glass prism is

• A. 2${}^{\circ }$
• B. 6${}^{\circ }$
• C. 8${}^{\circ }$
• D. 4${}^{\circ }$

Answer 1

Answer: (D)

4${}^{\circ }$

We have

$({\mu }_1-1)A_1+({\mu }_2-1)A_2=0$

$\frac{A_2}{A_1}=-\frac{{\mu }_1-1}{{\mu }_2-1}$
Where for crown, ${\mu }_1=(\frac{{\mu }_R+{\mu }_B}{2}=(\frac{1.51+1.49}{2})=1.5$

and for flint ${\mu }_2=(\frac{{\mu }_R+{\mu }_B}{2}=(\frac{1.77+1.73}{2})=1.75$

$⟹\frac{A_2}{A_1}=-\frac{1.5-1}{1.75-1}=0.667$
$⟹A_2=0.667\times 6=4^0$