A thin prism of angle $15^{\circ}$ made of glass of refractive index $\mu_1=1.5$ is combined with another pris

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 prism produces dispersion without deviation. The angle of the second prism should be:

Accepted Answer

1.  **Condition for Dispersion without Deviation:** For a combination of two thin prisms to produce dispersion without any net deviation, the mean deviation produced by the first prism must be equal and opposite to the mean deviation produced by the second prism.
2.  **Formula:** The deviation ($\delta$) produced by a thin prism of angle $A$ and refractive index $\mu$ is given by $\delta = (\mu - 1)A$.
3.  **Calculation:**
    *   For the first prism: $\delta_1 = (\mu_1 - 1)A_1 = (1.5 - 1) 	imes 15^{\circ} = 0.5 	imes 15^{\circ} = 7.5^{\circ}$.
    *   For the second prism: $\delta_2 = (\mu_2 - 1)A_2 = (1.75 - 1)A_2 = 0.75 A_2$.
    *   Equating the magnitudes for zero net deviation: $\delta_1 = \delta_2$.
    *   $7.5^{\circ} = 0.75 A_2$.
    *   $A_2 = \frac{7.5}{0.75} = 10^{\circ}$.

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