To solve the problem, we will follow these steps:
### Step 1: Calculate the reflected intensity of sunlight.
Given that the total energy density of sunlight incident on the solar panel is \( I = 50 \, \text{W/m}^2 \) and \( 25\% \) of it is reflected, we can calculate the reflected intensity \( I_R \).
\[
I_R = 0.25 \times I = 0.25 \times 50 \, \text{W/m}^2 = 12.5 \, \text{W/m}^2
\]
### Step 2: Calculate the absorbed intensity of sunlight.
The absorbed intensity \( I_A \) can be calculated by subtracting the reflected intensity from the total intensity.
\[
I_A = I - I_R = 50 \, \text{W/m}^2 - 12.5 \, \text{W/m}^2 = 37.5 \, \text{W/m}^2
\]
### Step 3: Calculate the pressure due to absorbed radiation.
The pressure \( P_A \) due to the absorbed radiation is given by the formula:
\[
P_A = \frac{I_A}{c}
\]
Substituting the values:
\[
P_A = \frac{37.5 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} = 1.25 \times 10^{-7} \, \text{N/m}^2
\]
### Step 4: Calculate the pressure due to reflected radiation.
The pressure \( P_R \) due to the reflected radiation is given by the formula:
\[
P_R = \frac{2I_R}{c}
\]
Substituting the values:
\[
P_R = \frac{2 \times 12.5 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} = \frac{25 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} = \frac{25}{3} \times 10^{-8} \, \text{N/m}^2 \approx 8.33 \times 10^{-8} \, \text{N/m}^2
\]
### Step 5: Calculate the total pressure on the solar panel.
The total pressure \( P \) on the solar panel is the sum of the pressures due to absorbed and reflected radiation.
\[
P = P_A + P_R = 1.25 \times 10^{-7} \, \text{N/m}^2 + 8.33 \times 10^{-8} \, \text{N/m}^2 = 2.083 \times 10^{-7} \, \text{N/m}^2
\]
### Step 6: Calculate the force exerted on the solar panel.
The force \( F \) exerted on a surface area \( A \) is given by:
\[
F = P \times A
\]
Given that \( A = 1 \, \text{m}^2 \):
\[
F = 2.083 \times 10^{-7} \, \text{N/m}^2 \times 1 \, \text{m}^2 = 2.083 \times 10^{-7} \, \text{N}
\]
### Final Answer
The force exerted on the \( 1 \, \text{m}^2 \) surface area of the solar panel is approximately \( 20.83 \times 10^{-8} \, \text{N} \).
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