The refracting angle of a prism is `40^(@)`. A ray of light is incident at angle `38^(@)` and passes in the position of minimum deviation. The angle of minimum deviation is

Options

A. `40^(@)`
B. `38^(@)`
C. `36^(@)`
D. `32^(@)`

Answer

To solve the problem, we will use the formula for the angle of minimum deviation in a prism. The steps are as follows:

### Step 1: Understand the given values
We are given:
- The refracting angle of the prism (A) = 40°
- The angle of incidence (I) = 38°

### Step 2: Use the formula for angle of minimum deviation
In the case of minimum deviation, the angle of incidence (I) is equal to the angle of emergence (E). The formula for the angle of minimum deviation (Δ) is given by:
\[ \Delta = I + E - A \]
Since \(I = E\) at minimum deviation, we can rewrite the formula as:
\[ \Delta = 2I - A \]

### Step 3: Substitute the known values into the formula
Now, substitute the values of I and A into the formula:
\[ \Delta = 2(38°) - 40° \]

### Step 4: Calculate the angle of minimum deviation
Now, perform the calculation:
\[ \Delta = 76° - 40° = 36° \]

### Step 5: Conclusion
The angle of minimum deviation (Δ) is 36°.

### Final Answer
The angle of minimum deviation is **36°**.

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