A beam of plane polarized light having flux `10^(-3)` Watt falls normally on polarizer of cross sectional area 3x10^(-4) m^2. Polarizer rotates with angular frequency of 31.4 rad/s. Energy of light passes through the polarizer per resolution will be

Options

A. `10^(-4) J`
B. `10^(-3) J`
C. `10^(-2) J`
D. `10^(-1) J`

Answer

To solve the problem, we need to find the energy of light passing through a rotating polarizer per revolution. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Data
- **Flux (F)** of the light beam: \( F = 10^{-3} \, \text{W} \)
- **Cross-sectional area (A)** of the polarizer: \( A = 3 \times 10^{-4} \, \text{m}^2 \)
- **Angular frequency (ω)** of the polarizer: \( \omega = 31.4 \, \text{rad/s} \)

### Step 2: Calculate the Intensity (I)
The intensity (I) of the light can be calculated using the formula:
\[ I = \frac{F}{A} \]
Substituting the values:
\[ I = \frac{10^{-3}}{3 \times 10^{-4}} = \frac{10}{3} \, \text{W/m}^2 \]

### Step 3: Determine the Intensity of Emergent Light
For a polarizer, the intensity of the emergent polarized light (I') is given by:
\[ I' = \frac{I_0}{2} \]
Where \( I_0 \) is the initial intensity. Thus:
\[ I' = \frac{10/3}{2} = \frac{5}{3} \, \text{W/m}^2 \]

### Step 4: Calculate the Time Period (T) for One Revolution
The time period (T) for one complete revolution is given by:
\[ T = \frac{2\pi}{\omega} \]
Substituting the value of ω:
\[ T = \frac{2\pi}{31.4} \approx \frac{6.28}{31.4} \approx 0.2 \, \text{s} \]

### Step 5: Calculate the Energy (E) Passing Through the Polarizer
The energy (E) passing through the polarizer in one revolution can be calculated using the formula:
\[ E = I' \cdot A \cdot T \]
Substituting the values:
\[ E = \left(\frac{5}{3}\right) \cdot (3 \times 10^{-4}) \cdot (0.2) \]
Calculating this:
\[ E = \frac{5}{3} \cdot 3 \times 10^{-4} \cdot 0.2 = 5 \times 10^{-4} \cdot 0.2 = 10^{-4} \, \text{J} \]

### Conclusion
The energy of light passing through the polarizer per revolution is:
\[ E = 10^{-4} \, \text{J} \]

### Final Answer
The correct option is **10^{-4} Joule**.

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