A medium has `n_v = 1.56, n_r=1.44`. Then its dispersive power is:

Options

A. `3//50`
B. `6//25`
C. 0.03
D. none of these

Explanation

To find the dispersive power of the medium, we will follow these steps:

### Step 1: Understand the formula for dispersive power
Dispersive power (ω) is defined as the ratio of the angular dispersion (Δθ) to the mean deviation (Dm) of the light passing through a prism. The formula is given by:
\[ \omega = \frac{\Delta \theta}{D_m} \]

### Step 2: Calculate the mean refractive index (μm)
The mean refractive index (μm) can be approximated as the average of the refractive indices of violet (μv) and red (μr) light:
\[ \mu_m = \frac{\mu_v + \mu_r}{2} \]
Given:
- \( \mu_v = 1.56 \)
- \( \mu_r = 1.44 \)

Substituting the values:
\[ \mu_m = \frac{1.56 + 1.44}{2} = \frac{3.00}{2} = 1.50 \]

### Step 3: Calculate the mean deviation (Dm)
The mean deviation (Dm) is given by:
\[ D_m = (\mu_m - 1) \cdot A \]
Where A is the angle of the prism. We will keep A as a variable for now.

### Step 4: Calculate the angular dispersion (Δθ)
The angular dispersion (Δθ) is given by:
\[ \Delta \theta = (\mu_v - \mu_r) \cdot A \]
Substituting the values of μv and μr:
\[ \Delta \theta = (1.56 - 1.44) \cdot A = 0.12 \cdot A \]

### Step 5: Substitute the values into the dispersive power formula
Now we can substitute Δθ and Dm into the dispersive power formula:
\[ \omega = \frac{\Delta \theta}{D_m} = \frac{0.12 \cdot A}{(1.50 - 1) \cdot A} \]
The angle A cancels out:
\[ \omega = \frac{0.12}{0.50} = \frac{12}{50} = \frac{6}{25} \]

### Final Answer
Thus, the dispersive power of the medium is:
\[ \omega = \frac{6}{25} \]

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