There is prism of refractive index 1.5 and prism angle `2 degree`. Find minimum deviation caused by this prism

Options

A. `1 deg`
B. `2 deg`
C. `1/3 deg`
D. `1/2 deg`

Answer

To find the minimum deviation caused by a prism with a refractive index of 1.5 and a prism angle of 2 degrees, we can use the formula for minimum deviation in terms of the refractive index and the prism angle.

### Step-by-step Solution:

1. **Identify the Given Values:**
- Refractive index (μ) = 1.5
- Prism angle (A) = 2 degrees

2. **Use the Formula for Minimum Deviation:**
The formula relating the refractive index, prism angle, and minimum deviation (D) is given by:
\[ \mu = \frac{\sin\left(\frac{A + D}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]
For small angles, we can use the approximation \(\sin x \approx x\) when x is in radians.

3. **Convert Angles to Radians:**
Since the angles are small, we can convert degrees to radians:
\[ A = 2 \text{ degrees} = \frac{2 \times \pi}{180} \text{ radians} = \frac{\pi}{90} \text{ radians} \]

4. **Approximate the Sine Functions:**
For small angles:
\[ \sin\left(\frac{A}{2}\right) \approx \frac{A}{2} = \frac{\pi/90}{2} = \frac{\pi}{180} \]
And for minimum deviation:
\[ \sin\left(\frac{A + D}{2}\right) \approx \frac{A + D}{2} \]

5. **Substituting into the Formula:**
Substitute the approximations into the formula:
\[ 1.5 = \frac{\frac{A + D}{2}}{\frac{A}{2}} \]
This simplifies to:
\[ 1.5 = \frac{A + D}{A} \]

6. **Rearranging the Equation:**
Rearranging gives:
\[ 1.5A = A + D \]
\[ D = 1.5A - A = 0.5A \]

7. **Calculating Minimum Deviation:**
Now substituting the value of A:
\[ D = 0.5 \times 2 = 1 \text{ degree} \]

### Final Answer:
The minimum deviation caused by the prism is **1 degree**.