A perfectly reflecting mirror has an area of `1cm^(2)` Light enery is allowed to fall on it 1 h at the rate of `10 W cm^(2)`. The force that acts on the mirror is

Options

A. `3.35 xx 10^(-8) N`
B. `6.7 xx 10^(-8) N`
C. `1.34 xx 10^(-7)N`
D. `2.4 xx 10^(-4) N`

Explanation

To find the force acting on a perfectly reflecting mirror when light energy falls on it, we can follow these steps:

### Step 1: Calculate the Energy Falling on the Mirror
Given that the light energy falls on the mirror at a rate of \(10 \, \text{W/cm}^2\) and the area of the mirror is \(1 \, \text{cm}^2\), we can calculate the power (energy per unit time) falling on the mirror.

\[ \text{Power} = \text{Intensity} \times \text{Area} \]

\[ \text{Power} = 10 \, \text{W/cm}^2 \times 1 \, \text{cm}^2 = 10 \, \text{W} \]

### Step 2: Calculate the Total Energy Over Time
The energy falling on the mirror over 1 hour (3600 seconds) can be calculated as follows:

\[ \text{Energy} = \text{Power} \times \text{Time} \]

\[ \text{Energy} = 10 \, \text{W} \times 3600 \, \text{s} = 36000 \, \text{J} \]

### Step 3: Calculate the Momentum of the Light
The momentum \(p\) associated with the energy \(E\) of the light can be expressed as:

\[ p = \frac{E}{c} \]

where \(c\) is the speed of light (\(c \approx 3 \times 10^8 \, \text{m/s}\)).

### Step 4: Calculate the Change in Momentum
Since the mirror is perfectly reflecting, the change in momentum \(\Delta p\) will be twice the momentum of the incoming light:

\[ \Delta p = 2p = 2 \left(\frac{E}{c}\right) \]

### Step 5: Calculate the Force
The force \(F\) acting on the mirror is given by the rate of change of momentum:

\[ F = \frac{\Delta p}{\Delta t} = \frac{2E}{c \cdot \Delta t} \]

Substituting \(\Delta t = 1 \, \text{second}\):

\[ F = \frac{2 \times 36000 \, \text{J}}{3 \times 10^8 \, \text{m/s}} = \frac{72000}{3 \times 10^8} \]

Calculating this gives:

\[ F = 2.4 \times 10^{-4} \, \text{N} \]

### Final Answer
Thus, the force that acts on the mirror is approximately \(2.4 \times 10^{-4} \, \text{N}\).

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