When an unpolarised light of inensity `I_0` is incident on a polarizing sheet, the intensity of the light which does not get transmittted is

Options

A. (a) Zero
B. (b) `I_0`
C. (c) `1/2I_0`
D. (d) `1/4I_0`

Explanation

To find the intensity of the light that does not get transmitted through a polarizing sheet when unpolarized light of intensity \( I_0 \) is incident on it, we can follow these steps:

### Step 1: Understand the nature of unpolarized light
Unpolarized light consists of waves vibrating in all possible planes perpendicular to the direction of propagation. When this light hits a polarizing sheet, only the component of light that aligns with the polarization direction of the sheet can pass through.

**Hint:** Remember that unpolarized light has multiple orientations of electric field vectors.

### Step 2: Apply Malus's Law
According to Malus's Law, when unpolarized light passes through a polarizer, the transmitted intensity \( I \) is given by:

\[ I = I_0 \cdot \cos^2 \theta \]

where \( I_0 \) is the initial intensity of the unpolarized light, and \( \theta \) is the angle between the light's polarization direction and the axis of the polarizer.

**Hint:** Malus's Law applies to polarized light; unpolarized light can be considered as having equal contributions from all angles.

### Step 3: Determine the intensity of transmitted light
For unpolarized light, when it first hits the polarizer, half of its intensity is effectively polarized. Thus, the intensity of the light that gets through the polarizer can be considered as:

\[ I_{\text{transmitted}} = \frac{I_0}{2} \cdot \cos^2 \theta \]

However, if we consider the case where the polarizer is aligned at \( \theta = 0^\circ \) (i.e., the light is aligned with the polarizer), then:

\[ I_{\text{transmitted}} = \frac{I_0}{2} \]

**Hint:** When unpolarized light hits a polarizer, it can be simplified to half the intensity being polarized.

### Step 4: Calculate the intensity of light that does not get transmitted
The intensity of the light that does not get transmitted through the polarizer can be found by subtracting the transmitted intensity from the initial intensity:

\[ I_{\text{not transmitted}} = I_0 - I_{\text{transmitted}} = I_0 - \frac{I_0}{2} = \frac{I_0}{2} \]

**Hint:** The intensity that does not get transmitted is simply the remaining half of the initial intensity.

### Final Answer
Thus, the intensity of the light that does not get transmitted through the polarizing sheet is:

\[ I_{\text{not transmitted}} = \frac{I_0}{2} \]