At what angle of incidence will the light reflected from glass`(mu=1.5)` be completely polarised

Options

A. `72.8^(@)`
B. `51.6^(@)`
C. `40.3^(@)`
D. `56.3^(@)`

Explanation

To find the angle of incidence at which light reflected from glass (with a refractive index \( \mu = 1.5 \)) is completely polarized, we can use Brewster's Law. Here’s the step-by-step solution:

### Step 1: Understand Brewster's Law
Brewster's Law states that the angle of incidence at which light is completely polarized upon reflection is given by the formula:
\[ \tan(\theta_P) = \frac{n_2}{n_1} \]
where:
- \( \theta_P \) is the polarizing angle,
- \( n_2 \) is the refractive index of the medium into which the light is entering (in this case, glass),
- \( n_1 \) is the refractive index of the medium from which the light is coming (in this case, air, which has an index of approximately 1).

### Step 2: Identify the Refractive Indices
From the problem, we know:
- \( n_2 = 1.5 \) (for glass),
- \( n_1 = 1.0 \) (for air).

### Step 3: Substitute the Values into Brewster's Law
Now, we substitute the values into the equation:
\[ \tan(\theta_P) = \frac{1.5}{1.0} = 1.5 \]

### Step 4: Calculate the Polarizing Angle
To find \( \theta_P \), we take the arctangent (inverse tangent) of 1.5:
\[ \theta_P = \tan^{-1}(1.5) \]

### Step 5: Use a Calculator to Find the Angle
Using a calculator, we find:
\[ \theta_P \approx 56.31^\circ \]

### Conclusion
The angle of incidence at which the light reflected from glass will be completely polarized is approximately:
\[ \theta_P \approx 56.3^\circ \]