When unpolarised light beam is incident from air onto glass ( n = 1.5) at the polarising angle

Options

A. Reflected beam is polarised 100 percent
B. Reflected and refracted beams are partially polarised
C. The reason for (a) is that almost all the light is reflected
D. All of the above

Answer

To solve the problem regarding the polarization of light when unpolarized light is incident from air onto glass at the polarizing angle, we can follow these steps:

### Step 1: Understand the Polarizing Angle
The polarizing angle (also known as Brewster's angle) is given by the formula:
\[ \tan(\theta_p) = \frac{n_2}{n_1} \]
where \( n_1 \) is the refractive index of the first medium (air, \( n_1 \approx 1 \)) and \( n_2 \) is the refractive index of the second medium (glass, \( n_2 = 1.5 \)).

### Step 2: Calculate the Polarizing Angle
Using the formula:
\[ \tan(\theta_p) = \frac{1.5}{1} = 1.5 \]
To find the polarizing angle \( \theta_p \):
\[ \theta_p = \tan^{-1}(1.5) \]
Using a calculator, we find:
\[ \theta_p \approx 56.31^\circ \]

### Step 3: Analyze the Incident Light
When unpolarized light hits the glass surface at the polarizing angle, the reflected light becomes polarized. According to the laws of reflection and refraction, the angle of incidence \( \theta_i \) equals the angle of reflection \( \theta_r \).

### Step 4: Determine the Polarization of the Reflected Light
At the polarizing angle, the reflected beam is 100% polarized. This means that all the reflected light waves vibrate in the same plane, perpendicular to the direction of propagation.

### Step 5: Conclusion
Thus, the reflected beam is fully polarized when unpolarized light is incident at the polarizing angle from air onto glass.

### Final Answer
The reflected beam is 100% polarized.

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