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 solve the problem, we need to find the angle of dispersion produced by the prism when light of wavelength 4000 Å is incident at a small angle. The parameters given are:

- Wavelength of light, \( \lambda = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} \)
- Apex angle of the prism, \( A = 4^\circ \)
- Refractive index for violet light, \( n_v = 1.5 \)
- Refractive index for red light, \( n_r = 1.48 \)

### Step 1: Calculate the angle of deviation for violet light

The formula for the angle of deviation \( D \) for a prism is given by:

\[ D = (n - 1) A \]

where \( n \) is the refractive index of the light passing through the prism and \( A \) is the apex angle of the prism.

For violet light:

\[ D_v = (n_v - 1) A = (1.5 - 1) \times 4^\circ \]

Calculating this gives:

\[ D_v = 0.5 \times 4^\circ = 2^\circ \]

### Step 2: Calculate the angle of deviation for red light

Using the same formula for red light:

\[ D_r = (n_r - 1) A = (1.48 - 1) \times 4^\circ \]

Calculating this gives:

\[ D_r = 0.48 \times 4^\circ = 1.92^\circ \]

### Step 3: Calculate the angle of dispersion

The angle of dispersion \( \Delta \) is given by the difference in the angles of deviation for violet and red light:

\[ \Delta = D_v - D_r \]

Substituting the values we calculated:

\[ \Delta = 2^\circ - 1.92^\circ = 0.08^\circ \]

### Final Answer

The angle of dispersion produced by the prism in this light is:

\[ \Delta = 0.08^\circ \]

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