A brilliant are lamp delivers a liminous flux of 100 w to a `1 cm ^(2)` absorber . The force due to radiation pressure is :

Options

A. `3.3xx10^(-4)` N
B. `16.5xx10^(-7)` N
C. `3.3xx10^(-6)` N
D. `3.3 xx10^(-7)` N

Explanation

To solve the problem of finding the force due to radiation pressure from a brilliant arc lamp delivering a luminous flux of 100 W to a 1 cm² absorber, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- Luminous flux (Power, P) = 100 W
- Area of the absorber = 1 cm² = \(1 \times 10^{-4} \, m^2\) (since \(1 \, cm^2 = 10^{-4} \, m^2\))

2. **Use the Formula for Radiation Pressure**:
- The radiation pressure (P_rad) can be calculated using the formula:
\[ P_{rad} = \frac{I}{c} \]
where \(I\) is the intensity of the radiation and \(c\) is the speed of light (\(c \approx 3 \times 10^8 \, m/s\)).

3. **Calculate the Intensity (I)**:
- Intensity is defined as power per unit area:
\[ I = \frac{P}{A} \]
- Substituting the values:
\[ I = \frac{100 \, W}{1 \times 10^{-4} \, m^2} = 1 \times 10^6 \, W/m^2 \]

4. **Calculate the Radiation Pressure**:
- Now substituting the intensity into the radiation pressure formula:
\[ P_{rad} = \frac{1 \times 10^6 \, W/m^2}{3 \times 10^8 \, m/s} = \frac{1}{3} \times 10^{-2} \, N/m^2 = 3.33 \times 10^{-3} \, N/m^2 \]

5. **Calculate the Force (F)**:
- The force due to radiation pressure can be calculated using:
\[ F = P_{rad} \times A \]
- Substituting the values:
\[ F = 3.33 \times 10^{-3} \, N/m^2 \times 1 \times 10^{-4} \, m^2 = 3.33 \times 10^{-7} \, N \]

### Final Answer:
The force due to radiation pressure is \(3.33 \times 10^{-7} \, N\).

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