A thin prism deviates an incident ray by `3.2^@`. If the refractive index of the prism is 2.6 then the angle of prism is

Options

A. `1^@`
B. `2^@`
C. `3^@`
D. `4^@`

Explanation

To find the angle of the prism (A) given the deviation (δ) and the refractive index (μ), we can use the formula for a thin prism:

\[ \mu = \frac{\sin\left(\frac{A + \delta}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

Since we are dealing with a thin prism, we can use the small angle approximation where \(\sin\theta \approx \theta\) when the angle is small. Thus, we can rewrite the equation as:

\[ \mu \approx \frac{\frac{A + \delta}{2}}{\frac{A}{2}} = \frac{A + \delta}{A} \]

Now, let's solve for A step by step:

### Step 1: Write down the known values
- Deviation (δ) = 3.2°
- Refractive index (μ) = 2.6

### Step 2: Substitute the known values into the equation
Using the formula derived above:

\[ 2.6 = \frac{A + 3.2}{A} \]

### Step 3: Cross-multiply to eliminate the fraction
\[ 2.6A = A + 3.2 \]

### Step 4: Rearrange the equation
Subtract A from both sides:

\[ 2.6A - A = 3.2 \]
\[ 1.6A = 3.2 \]

### Step 5: Solve for A
Divide both sides by 1.6:

\[ A = \frac{3.2}{1.6} = 2° \]

### Conclusion
The angle of the prism (A) is 2°.

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