A plane electromagnetic wave of intensity of `10 W//m^(2)` strikes a small mmirror of area `20 cm^(2)`, held perpendicular to the approcaching wave. The radiation froce on the mirror will be:

Options

A. `6.6xx10^(-11)` N
B. `1.33xx10^(-11)` N
C. `1.33xx10^(-10)` N
D. `6.6xx10^(-10)` N

Explanation

To solve the problem of finding the radiation force on a mirror struck by a plane electromagnetic wave, we can follow these steps:

### Step 1: Identify the given values
- Intensity of the electromagnetic wave, \( I = 10 \, \text{W/m}^2 \)
- Area of the mirror, \( A = 20 \, \text{cm}^2 = 20 \times 10^{-4} \, \text{m}^2 = 0.002 \, \text{m}^2 \)

### Step 2: Calculate the power incident on the mirror
The power \( P \) incident on the mirror can be calculated using the formula:
\[ P = I \times A \]
Substituting the values:
\[ P = 10 \, \text{W/m}^2 \times 0.002 \, \text{m}^2 = 0.02 \, \text{W} \]

### Step 3: Relate power to momentum change
The momentum \( p \) associated with the power can be calculated using the relationship between energy and momentum. The momentum change per second (force) can be calculated as:
\[ F = \frac{2P}{c} \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step 4: Substitute the values into the force equation
Substituting the calculated power into the force equation:
\[ F = \frac{2 \times 0.02 \, \text{W}}{3 \times 10^8 \, \text{m/s}} = \frac{0.04}{3 \times 10^8} \]

### Step 5: Calculate the force
Now, performing the calculation:
\[ F = \frac{0.04}{3 \times 10^8} = \frac{4 \times 10^{-2}}{3 \times 10^8} = \frac{4}{3} \times 10^{-10} \, \text{N} \]
Calculating this gives:
\[ F \approx 1.33 \times 10^{-10} \, \text{N} \]

### Final Answer
The radiation force on the mirror is approximately \( 1.33 \times 10^{-10} \, \text{N} \).

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