Question

A thin prism of angle $5^\circ $ made of glass of refractive index $\mu _{1}=1.5$ is combined with another prism of glass of refractive index $\mu _{2}=1.75$ . The combination of the prisms produces dispersion without deviation. The angle of the second prism should be

• A. $5^\circ $
• B. $7^\circ $
• C. $\frac{10 ^\circ }{3}$
• D. $1.2^\circ $

Answer 1

Answer: (C)

For dispersion without deviation
$\delta_{1}+\delta_{2}=0$
$\left(\mu_1-1\right) \mathrm{A}_1+\left(\mu_2-1\right) \mathrm{A}_2=0$
$A_2=-\frac{\left(\mu_1-1\right) A_1}{\left(\mu_2-1\right)}$
Substituting the given values, we get
$A _{2}=-\frac{\left(1 \cdot 5 - 1\right) 5 ^\circ }{\left(1 \cdot 75 - 1\right)}=-\frac{10 ^\circ }{3}$
The negative sign shows that the two prisms must be joined in opposition.