Light of wavelenght `4000 A` is incident at small angle on a prim of apex angle `4^(@)` . The prism has `n_(v)=1.5` and `n_(r)=1.48` . The angle of dispersion produced by the prism in this light is:

Options

A. `0.2^(@)`
B. `0.08^(@)`
C. `0.192^(@)`
D. none of these

Explanation

To find the angle of dispersion produced by the prism for light of wavelength 4000 Å (angstroms), we can use the formula for the angle of dispersion \( D \):

\[ D = A \cdot (n_v - n_r) \]

where:
- \( D \) is the angle of dispersion,
- \( A \) is the apex angle of the prism,
- \( n_v \) is the refractive index for violet light,
- \( n_r \) is the refractive index for red light.

### Step-by-Step Solution:

1. **Identify the given values:**
- Wavelength of light: \( \lambda = 4000 \, \text{Å} \) (not directly needed for this calculation)
- Apex angle of the prism: \( A = 4^\circ \)
- Refractive index for violet light: \( n_v = 1.5 \)
- Refractive index for red light: \( n_r = 1.48 \)

2. **Calculate the difference in refractive indices:**
\[ n_v - n_r = 1.5 - 1.48 = 0.02 \]

3. **Substitute the values into the dispersion formula:**
\[ D = A \cdot (n_v - n_r) = 4^\circ \cdot 0.02 \]

4. **Perform the multiplication:**
\[ D = 4 \cdot 0.02 = 0.08^\circ \]

5. **Conclusion:**
The angle of dispersion produced by the prism for the given light is \( 0.08^\circ \).

### Final Answer:
The angle of dispersion produced by the prism in this light is \( 0.08^\circ \).

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