The critical angle for diamond (refractive index = 2) is

Options

A. About `60^@`
B. `60^@`
C. `45^@`
D. `30^@`

Answer

To find the critical angle for diamond with a refractive index of 2, we can follow these steps:

### Step 1: Understand the concept of critical angle
The critical angle is defined as the angle of incidence in a denser medium (like diamond) at which the angle of refraction in a less dense medium (like air) is 90 degrees.

### Step 2: Use the formula for critical angle
The relationship between the refractive index (μ) of the denser medium and the critical angle (C) is given by the formula:
\[ \mu = \frac{1}{\sin C} \]
where:
- μ is the refractive index of the denser medium (diamond in this case),
- C is the critical angle.

### Step 3: Substitute the given values
In this case, the refractive index of diamond is given as 2. So we can substitute this value into the formula:
\[ 2 = \frac{1}{\sin C} \]

### Step 4: Solve for sin C
Rearranging the equation gives us:
\[ \sin C = \frac{1}{2} \]

### Step 5: Find the critical angle
Now, we need to determine the angle whose sine is \( \frac{1}{2} \). From trigonometry, we know that:
\[ \sin 30^\circ = \frac{1}{2} \]
Thus, the critical angle \( C \) is:
\[ C = 30^\circ \]

### Conclusion
The critical angle for diamond is \( 30^\circ \).

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