A prism of angle `A = 1^(@)` has a refractive index `mu = 1.5` . A good estimate for the minimum angle of deviation ( in degrees ) is close to N/10 value of N is ________ .

Answer

To solve the problem, we need to find the minimum angle of deviation (δm) for a prism with a small angle of prism (A = 1°) and a refractive index (μ = 1.5). The relationship we will use is:

\[ \delta_m = (\mu - 1) \cdot A \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Angle of prism, \( A = 1^\circ \)
- Refractive index, \( \mu = 1.5 \)

2. **Convert the angle from degrees to radians (if necessary)**:
- Since we are working with small angles, we can use the angle in degrees directly in our formula.

3. **Use the formula for minimum angle of deviation**:
- Substitute the values into the formula:
\[ \delta_m = (\mu - 1) \cdot A \]
\[ \delta_m = (1.5 - 1) \cdot 1^\circ \]
\[ \delta_m = 0.5 \cdot 1^\circ \]

4. **Calculate the minimum angle of deviation**:
- This gives us:
\[ \delta_m = 0.5^\circ \]

5. **Express the result in terms of N/10**:
- We need to express \( 0.5^\circ \) in the form of \( N/10 \):
\[ 0.5^\circ = \frac{5}{10}^\circ \]
- Thus, we can equate:
\[ \frac{N}{10} = \frac{5}{10} \]
- From this, we find:
\[ N = 5 \]

### Final Answer:
The value of \( N \) is **5**.