A thin prism of angle `6^(@)` made up of glass of refractive index 1.5 is combined with anorher prism made up of glass of refractive index 1.75 to produce dispersion without deviation. The angle of second prism is

Options

A. `7^(@)`
B. `9^(@)`
C. `4^(@)`
D. `5^(@)`

Explanation

To solve the problem of finding the angle of the second prism that, when combined with the first prism, produces dispersion without deviation, we can follow these steps:

### Step 1: Understand the Given Data
We have:
- Angle of the first prism (A1) = 6 degrees
- Refractive index of the first prism (μ1) = 1.5
- Refractive index of the second prism (μ2) = 1.75
- We need to find the angle of the second prism (A2).

### Step 2: Set Up the Condition for Dispersion without Deviation
For two prisms to produce dispersion without deviation, the following condition must hold:
\[ \delta_1 - \delta_2 = 0 \]
This implies:
\[ \delta_1 = \delta_2 \]
Using the formula for deviation for a thin prism, we have:
\[ \delta = (\mu - 1) \cdot A \]
Thus, for the two prisms:
\[ (\mu_1 - 1) \cdot A_1 = (\mu_2 - 1) \cdot A_2 \]

### Step 3: Substitute the Known Values
Substituting the values we have:
\[ (1.5 - 1) \cdot 6 = (1.75 - 1) \cdot A_2 \]
This simplifies to:
\[ 0.5 \cdot 6 = 0.75 \cdot A_2 \]
\[ 3 = 0.75 \cdot A_2 \]

### Step 4: Solve for A2
Now, we can solve for A2:
\[ A_2 = \frac{3}{0.75} \]
Calculating this gives:
\[ A_2 = \frac{3 \times 100}{75} = \frac{300}{75} = 4 \text{ degrees} \]

### Final Answer
The angle of the second prism (A2) is **4 degrees**.

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