Arrange the ascending order of polarising angles for air-glass, air-water, and water-glass interfaces?

Options

A. water-glass, air-water, air-glass
B. air-water, air-glass, water-glass
C. air-glass, air-water, water-glass
D. air-water, water-glass, air-glass

Answer

To find the ascending order of polarizing angles for the air-glass, air-water, and water-glass interfaces, we will use the formula for the polarizing angle (also known as Brewster's angle), which is given by:

\[ \tan(\theta_p) = \frac{n_2}{n_1} \]

where \( n_1 \) is the refractive index of the first medium and \( n_2 \) is the refractive index of the second medium.

### Step 1: Identify the refractive indices
- Refractive index of air (\( n_{air} \)) = 1.00
- Refractive index of water (\( n_{water} \)) = 1.33
- Refractive index of glass (\( n_{glass} \)) = 1.50

### Step 2: Calculate the polarizing angle for air-glass interface
Using the formula:
\[ \tan(\theta_{p1}) = \frac{n_{glass}}{n_{air}} = \frac{1.50}{1.00} = 1.50 \]
Now, we find \( \theta_{p1} \):
\[ \theta_{p1} = \tan^{-1}(1.50) \approx 56.31^\circ \]

### Step 3: Calculate the polarizing angle for air-water interface
Using the formula:
\[ \tan(\theta_{p2}) = \frac{n_{water}}{n_{air}} = \frac{1.33}{1.00} = 1.33 \]
Now, we find \( \theta_{p2} \):
\[ \theta_{p2} = \tan^{-1}(1.33) \approx 53.06^\circ \]

### Step 4: Calculate the polarizing angle for water-glass interface
Using the formula:
\[ \tan(\theta_{p3}) = \frac{n_{glass}}{n_{water}} = \frac{1.50}{1.33} \approx 1.13 \]
Now, we find \( \theta_{p3} \):
\[ \theta_{p3} = \tan^{-1}(1.13) \approx 48.37^\circ \]

### Step 5: Arrange the angles in ascending order
Now we have the polarizing angles:
- \( \theta_{p1} \) (air-glass) ≈ 56.31°
- \( \theta_{p2} \) (air-water) ≈ 53.06°
- \( \theta_{p3} \) (water-glass) ≈ 48.37°

Arranging these in ascending order:
1. Water-glass: \( \theta_{p3} \approx 48.37^\circ \)
2. Air-water: \( \theta_{p2} \approx 53.06^\circ \)
3. Air-glass: \( \theta_{p1} \approx 56.31^\circ \)

### Final Answer
The ascending order of polarizing angles is:
1. Water-glass
2. Air-water
3. Air-glass