In determining the angle of minimum deviation for a given prism, a graph is plotted between the angle of incidence (j) and the angle of deviation `(delta)`. Which of the following graphs will correctly

Options

A.
B.
C.
D.

Answer

To determine the angle of minimum deviation for a given prism, we need to analyze the relationship between the angle of incidence (j) and the angle of deviation (δ). Here’s a step-by-step solution to the problem:

### Step 1: Understand the relationship
The angle of minimum deviation occurs when the angle of incidence equals the angle of emergence. This means that at this point, the light ray passes symmetrically through the prism.

### Step 2: Use the formula for minimum deviation
The formula relating the refractive index (μ) of the prism, the angle of minimum deviation (D), and the angle of the prism (A) is given by:
\[ \mu = \frac{\sin\left(\frac{D + A}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]
This formula indicates that as the angle of incidence increases, the angle of deviation will change until it reaches a minimum value.

### Step 3: Plotting the graph
When plotting the graph of angle of incidence (j) on the x-axis and angle of deviation (δ) on the y-axis:
- The graph will not be symmetrical about the minimum deviation point.
- It will show a gradual increase in deviation as the angle of incidence increases, reaching a minimum deviation at a specific angle, after which the deviation will start to increase again.

### Step 4: Identify the characteristics of the graph
The graph will have the following characteristics:
- It will be tilted towards the right side.
- The minimum deviation point will be where the angle of incidence equals the angle of emergence.
- The graph will not be a perfect parabola.

### Step 5: Choose the correct option
After analyzing the given options (A, B, C, D), we find that option D correctly represents the relationship between angle of incidence and angle of deviation for a prism.

### Final Answer
Thus, the correct answer is **Option D**.

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