A small angled prism `(mu = 1.62)` gives a deviation of `4.8`. Calculate the angle of prism.

Options

A. `5^(@)`
B. `6.36^(@)`
C. `3^(@)`
D. `7.74^(@)`

Explanation

To solve the problem of finding the angle of the prism given the refractive index and the angle of deviation, we can follow these steps:

### Step 1: Write down the known values
- Refractive index (μ) = 1.62
- Angle of deviation (D) = 4.8 degrees

### Step 2: Use the formula for the angle of deviation in a small angled prism
The formula for the angle of deviation (D) in a small angled prism is given by:
\[ D = (\mu - 1) \times A \]
where:
- D is the angle of deviation,
- μ is the refractive index,
- A is the angle of the prism.

### Step 3: Rearrange the formula to solve for the angle of the prism (A)
We can rearrange the formula to isolate A:
\[ A = \frac{D}{\mu - 1} \]

### Step 4: Substitute the known values into the equation
Now, substitute the values we have into the rearranged formula:
\[ A = \frac{4.8}{1.62 - 1} \]
\[ A = \frac{4.8}{0.62} \]

### Step 5: Calculate the angle of the prism
Now, perform the calculation:
\[ A = \frac{4.8}{0.62} \approx 7.74 \text{ degrees} \]

### Conclusion
The angle of the prism (A) is approximately 7.74 degrees.

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