Question

When a beam of white light enters into an optical prism, the most deviated colour is ________.

• A. green
• B. violet
• C. yellow
• D. red
• E. blue

Hint:

VIBGYOR: Violet deviates most (shortest $\lambda$), Red deviates least (longest $\lambda$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
This question is about the phenomenon of dispersion of light. When white light passes through a prism, it splits into its constituent colors (the spectrum). This happens because the refractive index of the prism's material is different for different wavelengths (colors) of light. The amount a light ray bends, or deviates, depends on this refractive index.
Step 2: Key Formula or Approach
According to Cauchy's relation, the refractive index (\(n\)) of a transparent material is a function of the wavelength (\(\lambda\)) of light. For visible light, a good approximation is that the refractive index is inversely related to the wavelength:
\[ n \approx A + \frac{B}{\lambda^2} \] This means that shorter wavelengths have a higher refractive index.
The angle of deviation (\(\delta\)) for a prism is a function of the refractive index. For a prism with a small apex angle A, the deviation is approximately \(\delta \approx (n-1)A\).
In general, a higher refractive index (\(n\)) leads to a larger angle of deviation (\(\delta\)).
So, the deviation is inversely related to the wavelength: \(\delta \propto (n-1) \propto 1/\lambda^2\).
Step 3: Detailed Explanation
1. Wavelengths of Visible Light:
The colors of the visible spectrum, in order of increasing wavelength, are:
Violet - Indigo - Blue - Green - Yellow - Orange - Red (VIBGYOR)
- Violet has the shortest wavelength (\(\lambda_{violet}\) is minimum).
- Red has the longest wavelength (\(\lambda_{red}\) is maximum).
2. Relation between Wavelength, Refractive Index, and Deviation:
- Since the refractive index (\(n\)) is higher for shorter wavelengths, the prism's glass has the highest refractive index for violet light (\(n_{violet}\) is maximum) and the lowest for red light (\(n_{red}\) is minimum).
- Since the angle of deviation (\(\delta\)) increases with the refractive index, the deviation will be greatest for the color with the highest refractive index.
- Therefore, violet light is deviated the most.
- Conversely, red light is deviated the least.
Step 4: Final Answer
The most deviated colour is violet.