Question

The dispersive power of a prism depends on

• A. Angle of incidence
• B. Nature of material of prism
• C. Refracting angle of prism
• D. Angle of prism

Hint:

A key takeaway is that \textit{dispersion} (the separation of colors) depends on both the prism's angle and the material, but \textit{dispersive power} is a specific ratio that is an intrinsic property of the material alone. For example, a flint glass prism has a higher dispersive power than a crown glass prism, regardless of their shapes.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Dispersive power (\(\omega\)) is a property of the material of a prism that quantifies its ability to separate white light into its constituent colors (dispersion). It is defined as the ratio of the angular dispersion (the difference in deviation angles for two extreme colors, typically violet and red) to the deviation of a mean color (typically yellow).
Step 2: Key Formula or Approach:
The formula for dispersive power (\(\omega\)) is: \[ \omega = \frac{\text{Angular Dispersion}}{\text{Mean Deviation}} = \frac{\delta_V - \delta_R}{\delta_Y} \] For a prism with a small angle \(A\), the angle of deviation \(\delta\) is given by \(\delta = (\mu - 1)A\), where \(\mu\) is the refractive index of the material.
Substituting this into the formula for \(\omega\): \[ \omega = \frac{(\mu_V - 1)A - (\mu_R - 1)A}{(\mu_Y - 1)A} \] The prism angle \(A\) cancels out from the numerator and the denominator: \[ \omega = \frac{\mu_V - \mu_R}{\mu_Y - 1} \] Step 3: Detailed Explanation:
The final expression, \(\omega = \frac{\mu_V - \mu_R}{\mu_Y - 1}\), shows that the dispersive power depends only on the refractive indices of the prism's material for different wavelengths of light (\(\mu_V, \mu_R, \mu_Y\)). The refractive index is an intrinsic property of the material itself.
Therefore, the dispersive power depends on the nature of the material of the prism. It does not depend on the geometric properties of the prism, such as its angle (\(A\)), nor on how the light enters it, such as the angle of incidence.
Step 4: Final Answer:
Since dispersive power is determined solely by the refractive indices of the medium, it is a characteristic property of the material of the prism. Therefore, option (B) is correct.