Refraction by Prism: Practice Problem & Solution
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: (2011 Mains)
Solution Explained:
To solve this problem, we apply the core principles of Refraction by Prism. Understanding the underlying formula is key to arriving at the correct answer below:
For dispersion without deviation, the net deviation is zero, so $(\mu_1 - 1)A_1 = (\mu_2 - 1)A_2$. Substituting the given values: $(1.5 - 1)(15^\circ) = (1.75 - 1)A_2$. This gives $0.5 \times 15^\circ = 0.75 A_2$, which simplifies to $7.5^\circ = 0.75 A_2$, so $A_2 = 10^\circ$.
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