A thin prism of angle $15^{\circ}$ made of glass of refractive index $\mu_{1}=1.5$ is combined with

Question

A thin prism of angle $15^{\circ}$ 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\

Professor PC Thomas Classes · Answer

(c) : For dispersion without deviation $$ \begin{aligned} & \delta_{1}+\delta_{2}=0 \ & \left(\mu_{1}-1ight) A_{1}+\left(\mu_{2}-1ight) A_{2}=0 \ & A_{2}=-\frac{\left(\mu_{1}-1ight) A_{1}}{\left(\mu_{2}-1ight)} \end{aligned} $$ Substituting the given values, we get $$ A_{2}=-\frac{(1.5-1) 15^{\circ}}{(1.75-1)}=-10^{\circ} $$ Negative sign shows that two prisms must be joined in opposition.\