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

Explanation

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

### Step 1: Write down the deviation formula for a prism.
The formula for the deviation (Δ) produced by a prism is given by:
\[ \Delta = (\mu - 1) \cdot A \]
where:
- Δ is the angle of deviation,
- μ is the refractive index of the prism,
- A is the angle of the prism.

### Step 2: Substitute the known values into the formula.
From the problem, we know:
- μ = 1.62
- Δ = 4.8 degrees

Substituting these values into the deviation formula gives us:
\[ 4.8 = (1.62 - 1) \cdot A \]

### Step 3: Simplify the equation.
Calculate (μ - 1):
\[ 1.62 - 1 = 0.62 \]
Now the equation becomes:
\[ 4.8 = 0.62 \cdot A \]

### Step 4: Solve for the angle of the prism (A).
To find A, we rearrange the equation:
\[ A = \frac{4.8}{0.62} \]
Calculating this gives:
\[ A \approx 7.74 \text{ degrees} \]

### Final Answer:
The angle of the prism (A) is approximately **7.74 degrees**.

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