Question

Monochromatic light of wavelength 6000 Å incidents on a small angled prism. If the angle of the prism is 6°, the refractive indices of the material of the prism for violet and red lights are respectively 1.52 and 1.48, then the angle of dispersion produced for this incident light is

• A. 30°
• B. 36°
• C. 0.24°
• D. 0°
  \textit{Note: The provided options in the source material seem to have a typo. Option (C) is likely intended to be 0.24°. The solution below calculates the correct physical value.}

Hint:

In physics problems, if your calculated answer is physically reasonable but differs from the options by a factor of 10, 100, etc., double-check for a decimal point error in the options. Here, \(6 \times 0.04\) is clearly 0.24, making 24° a very likely typo.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Angular dispersion is the difference in the angles of deviation for two different wavelengths (colors) of light after passing through a dispersive medium like a prism. For a prism with a small angle, the deviation itself is small, and a simplified formula can be used.
Step 2: Key Formula or Approach:
For a small-angled prism, the angle of deviation \(\delta\) is given by:
\[ \delta = A(n-1) \] where \(A\) is the angle of the prism and \(n\) is the refractive index of the material.
The angular dispersion \(\theta\) between violet and red light is the difference in their deviations:
\[ \theta = \delta_v - \delta_r = A(n_v - 1) - A(n_r - 1) = A(n_v - n_r) \] The wavelength of the incident light (6000 Å) is not needed to calculate the angular dispersion between violet and red, as their refractive indices are already given.
Step 3: Detailed Explanation:
We are given the following values:
- Angle of the prism, \(A = 6^\circ\).
- Refractive index for violet light, \(n_v = 1.52\).
- Refractive index for red light, \(n_r = 1.48\).
Using the formula for angular dispersion:
\[ \theta = A(n_v - n_r) \] \[ \theta = 6^\circ (1.52 - 1.48) \] \[ \theta = 6^\circ (0.04) \] \[ \theta = 0.24^\circ \] Step 4: Final Answer:
The angle of dispersion is \(0.24^\circ\). The given options are numerically incorrect, likely due to a typographical error in the question paper. Option (C), which is listed as 24°, is probably meant to be 0.24°. Based on the calculation, the correct value is 0.24°.