The angle between pass axis of polarizer and analyser is `45^(@)`. The percentage of polarized light passing through analyser is

Options

A. `75%`
B. `25%`
C. `50%`
D. `100%`

Answer

To solve the problem of finding the percentage of polarized light passing through the analyzer when the angle between the pass axis of the polarizer and analyzer is \(45^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The intensity of light passing through a polarizer is given by Malus's Law, which states:
\[ I = I_0 \cos^2 \phi \]
where \(I\) is the intensity of the transmitted light, \(I_0\) is the intensity of the incident light, and \(\phi\) is the angle between the light's polarization direction and the axis of the polarizer.

2. **Identify the Angle**: In this case, the angle \(\phi\) between the pass axis of the polarizer and the analyzer is given as \(45^\circ\).

3. **Calculate \(\cos^2 \phi\)**: We need to calculate \(\cos^2(45^\circ)\):
\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \]
Therefore,
\[ \cos^2(45^\circ) = \left(\frac{1}{\sqrt{2}}\right)^2 = \frac{1}{2} \]

4. **Find the Ratio of Intensities**: According to Malus's Law, the ratio of the transmitted intensity \(I\) to the incident intensity \(I_0\) is:
\[ \frac{I}{I_0} = \cos^2(45^\circ) = \frac{1}{2} \]

5. **Convert to Percentage**: To find the percentage of polarized light passing through the analyzer, we multiply the ratio by 100:
\[ \text{Percentage} = \left(\frac{I}{I_0}\right) \times 100 = \frac{1}{2} \times 100 = 50\% \]

### Final Answer:
The percentage of polarized light passing through the analyzer is **50%**.

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