Two polaroids are crossed to each other. One of them is rotated through `60^(@)`, what % age of incident unpolarised light will pass through the system ?

Options

A. `37.5%`
B. `40%`
C. `20%`
D. `30%`

Explanation

To solve the problem of how much unpolarized light will pass through a system of two crossed polaroids when one is rotated by \(60^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Setup:**
- Initially, we have two polaroids crossed at \(90^\circ\). This means that the transmission axes of the two polaroids are perpendicular to each other.

2. **Rotation of One Polaroid:**
- One of the polaroids is rotated by \(60^\circ\). Therefore, the angle between the transmission axes of the two polaroids becomes:
\[ \text{New angle} = 90^\circ - 60^\circ = 30^\circ \]

3. **Applying Malus's Law:**
- Malus's Law states that when unpolarized light passes through a polarizer, the intensity \(I\) of the transmitted light is given by:
\[ I = I_0 \cos^2(\theta) \]
where \(I_0\) is the intensity of the incident light and \(\theta\) is the angle between the light's polarization direction and the axis of the polarizer.

4. **Intensity After First Polaroid:**
- The intensity of the light after passing through the first polaroid (which is initially unpolarized) is:
\[ I_1 = \frac{I_0}{2} \]
- This factor of \(\frac{1}{2}\) comes from the fact that unpolarized light passing through a polarizer results in half the intensity being transmitted.

5. **Intensity After Second Polaroid:**
- Now, the light that passes through the first polaroid (with intensity \(I_1\)) encounters the second polaroid. The angle between the light's polarization direction (after the first polaroid) and the axis of the second polaroid is \(30^\circ\).
- Using Malus's Law again:
\[ I_2 = I_1 \cos^2(30^\circ) = \frac{I_0}{2} \left(\frac{\sqrt{3}}{2}\right)^2 \]
- Simplifying this:
\[ I_2 = \frac{I_0}{2} \cdot \frac{3}{4} = \frac{3I_0}{8} \]

6. **Calculating the Percentage of Incident Light:**
- To find the percentage of the incident unpolarized light that passes through the system, we calculate:
\[ \text{Percentage} = \left(\frac{I_2}{I_0}\right) \times 100 = \left(\frac{3I_0/8}{I_0}\right) \times 100 = \frac{3}{8} \times 100 = 37.5\% \]

### Final Answer:
The percentage of incident unpolarized light that will pass through the system is **37.5%**.