Question

A thin prism, of prism angle ${15}^0$ made of glass of refractive index ${\mu }_1$ = 1.5 is combined with another prism of the glass of refractive index ${\mu }_2$ = 1.75. The combination of the prism produces dispersion without deviation. The angle of the second prism should be

• A. 20
• B. 15
• C. 10
• D. 5

Answer 1

Answer: (C)

10

Angle of prism of first prism $A_1={15}^o$

Refractive index of first prism ${\mu }_1=1.5$

Refractive index of first prism ${\mu }_2=1.75$

For dispersion without deviation, ${\delta }_{net}=0$

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

OR $A_2=\frac{{\mu }_1-1}{{\mu }_2-1}{A}_1$

$\therefore$ $A_2=\frac{1.5-1}{1.75-1}\times 15={10}^o$