A thin prism of `5^@` angle gives a deviation of `3.2^@`. What is the value of refraction index of the material of the prism?

Options

A. `mu` = 2.12
B. `mu` = 1.71
C. `mu` = 1.64
D. `mu` = 3.11

Answer

To find the refractive index (μ) of the material of the prism, we can use the formula that relates the angle of the prism (A), the angle of deviation (D), and the refractive index:

\[ \mu - 1 = \frac{D}{A} \]

Where:
- \( \mu \) is the refractive index,
- \( D \) is the angle of deviation,
- \( A \) is the angle of the prism.

Given:
- Angle of prism, \( A = 5^\circ \)
- Angle of deviation, \( D = 3.2^\circ \)

### Step 1: Substitute the values into the formula
We can substitute the given values into the formula:

\[ \mu - 1 = \frac{3.2}{5} \]

### Step 2: Calculate the right-hand side
Now, we calculate the right-hand side:

\[ \mu - 1 = 0.64 \]

### Step 3: Solve for μ
Now, we can solve for \( \mu \):

\[ \mu = 1 + 0.64 \]

\[ \mu = 1.64 \]

### Conclusion
The value of the refractive index of the material of the prism is \( \mu = 1.64 \).

---