Deviation of `5^(@)` is observed from a prism whose angle is small and whose refractive index is 1.5 The angle of prism is

Options

A. `7.5^(@)`
B. `10^(@)`
C. `5^(@)`
D. `3.3^(@)`

Answer

To find the angle of the prism given the deviation and the refractive index, we can use the formula for small angle prisms. Here’s a step-by-step solution:

### Step 1: Write down the formula for deviation in a thin prism.
For a thin prism, the deviation (D) is given by the formula:
\[ D = (\mu - 1) \cdot A \]
where:
- \( D \) = angle of deviation
- \( \mu \) = refractive index of the prism
- \( A \) = angle of the prism

### Step 2: Substitute the known values into the formula.
We are given:
- \( D = 5^\circ \)
- \( \mu = 1.5 \)

Substituting these values into the formula gives:
\[ 5 = (1.5 - 1) \cdot A \]

### Step 3: Simplify the equation.
Calculate \( (1.5 - 1) \):
\[ 1.5 - 1 = 0.5 \]

Now, substitute this back into the equation:
\[ 5 = 0.5 \cdot A \]

### Step 4: Solve for the angle of the prism (A).
To find \( A \), divide both sides of the equation by 0.5:
\[ A = \frac{5}{0.5} \]

Calculating this gives:
\[ A = 10^\circ \]

### Step 5: State the final answer.
The angle of the prism \( A \) is \( 10^\circ \).