A prism of certain angle deviates the red and blue rays by 8^∘ and 12^∘ respectively. Another pr

step 1 For this question, we know that dispersive power is equal to muv minus mu r divide by mu y minus

A prism of certain angle deviates the red and blue rays by...

A prism of certain angle deviates the red and blue rays by $8^{\circ}$ and $12^{\circ}$ respectively. Another prism of the same prism angle deviates the red and blue ray by $10^{\circ}$ and $14^{\circ}$ respectively. The prism are small angle and made of different materials. The dispersive powers of the materials of the prisms are in the ratio (A) $5: 6$ (B) $9: 11$ (C) $6: 5$ (D) $11: 9$

Key Concepts

Prism Deviation

When light passes through a prism, it bends (or deviates) due to the change in speed as it enters and exits the material. The deviation depends on the refractive index of the material as well as the prism’s apex angle. In practical problems, especially at small angles, the deviations for different wavelengths (colors) are proportional to the difference of the refractive index from unity, which leads directly to calculations of deviation differences for red and blue light.

Small-Angle Approximation

Under the assumption of small angles, trigonometric functions (such as sine and tangent) can be approximated by the angle itself when measured in radians. This simplification allows us to linearly relate the deviation produced by the prism to the prism’s apex angle and the refractive index (via the formula ? ? (n ? 1)A). Such approximations make it easier to compare how different wavelengths of light are deviated in an optical system.

Dispersive Power

The dispersive power of a material quantifies its ability to separate light into its constituent wavelengths. It is typically defined as the relative difference between the refractive indices for two different wavelengths (for example, blue and red) divided by a measure of the overall refractive effect (often taken as the difference for an intermediate color). This concept is key to understanding and comparing how different materials spread out or 'disperse' light, and is instrumental in solving problems involving multiple prisms made of distinct materials.

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