Suppose a small angled prism of `6^(@)` deviates a ray through `3^(@)`, then the refractive index is

Options

A. 1.62
B. 1.33
C. 1.5
D. 1.72

Answer

To find the refractive index (μ) of a small angled prism that deviates a ray through a certain angle, we can use the formula related to prism deviation. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Angle of the prism (A) = 6 degrees
- Angle of deviation (δ) = 3 degrees

### Step 2: Use the formula for deviation in a prism
The relationship between the angle of the prism (A), the angle of deviation (δ), and the refractive index (μ) is given by the formula:
\[ \delta = A(\mu - 1) \]

### Step 3: Substitute the known values into the formula
Substituting the values of A and δ into the formula:
\[ 3 = 6(\mu - 1) \]

### Step 4: Simplify the equation
Now, we will simplify the equation:
\[ 3 = 6\mu - 6 \]

### Step 5: Rearrange the equation to solve for μ
Adding 6 to both sides:
\[ 3 + 6 = 6\mu \]
\[ 9 = 6\mu \]

### Step 6: Divide both sides by 6 to isolate μ
\[ \mu = \frac{9}{6} \]

### Step 7: Simplify the fraction
\[ \mu = 1.5 \]

### Conclusion
The refractive index of the prism is **1.5**.

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