The critical angle for glass-air interface is :

Options

A. `24^(@)`
B. `48^(@)`
C. `42^(@)`
D. `45^(@)`

Answer

To find the critical angle for the glass-air interface, we can follow these steps:

### Step 1: Understand the concept of critical angle
The critical angle is the angle of incidence above which total internal reflection occurs when light travels from a denser medium (glass) to a less dense medium (air).

### Step 2: Use the formula for critical angle
The formula for the critical angle (Ic) is given by:
\[ \sin(I_c) = \frac{n_2}{n_1} \]
where \( n_1 \) is the refractive index of the denser medium (glass) and \( n_2 \) is the refractive index of the less dense medium (air).

### Step 3: Identify the refractive indices
For glass, the refractive index \( n_1 \) is approximately \( \frac{3}{2} \) (or 1.5), and for air, the refractive index \( n_2 \) is approximately 1.

### Step 4: Substitute the values into the formula
Using the values:
\[ \sin(I_c) = \frac{n_2}{n_1} = \frac{1}{\frac{3}{2}} = \frac{2}{3} \]

### Step 5: Calculate the critical angle
Now, we need to find the angle whose sine is \( \frac{2}{3} \):
\[ I_c = \sin^{-1}\left(\frac{2}{3}\right) \]

### Step 6: Use a calculator to find the angle
Calculating this gives:
\[ I_c \approx 41.81^\circ \]

### Step 7: Round to the nearest degree
Rounding this value gives us:
\[ I_c \approx 42^\circ \]

### Final Answer
Thus, the critical angle for the glass-air interface is approximately **42 degrees**.

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