9. A laser emits light when electrons are stimulated to fall from a high energy level to a lower energy level - Scottish Highers Physics - Question 9 - 2019

Given the diameter of the spot of light is $8.00 \times 10^{-4} \, m$, we can first determine the area of the spot:

$A = \pi r^2 = \pi \left(\frac{d}{2}\right)^2 = \pi \left(\frac{8.00 \times 10^{-4}}{2}\right)^2 = \pi (4.00 \times 10^{-4})^2 \approx 5.03 \times 10^{-7} \, m^2$

Now, knowing the irradiance $I$ is given as $9950 \, W m^{-2}$, we can find the power $P$ of the laser beam using the relationship: $P = I \times A$ Substituting in the values:

$P = 9950 \times 5.03 \times 10^{-7} \approx 5.00 \times 10^{-3} \, W$ Therefore, the power of the laser beam is approximately $5.00 \times 10^{-3} \, W$.

To verify the inverse square law using the described apparatus, the student should follow these steps:

1. Setup: Position the light source at a known height and distance from the light sensor. The distance should be precisely measured.

2. Irradiance Measurement: Use the light sensor to measure the irradiance $I$ at different distances $d$ from the light source. Record these values systematically.

3. Adjust Distance: Move the sensor to various distances from the light source, ensuring measurements are taken at consistent intervals.

4. Data Collection: For each distance, calculate the corresponding irradiance and record the data.

5. Analysis: Graph the collected data with $I$ on the y-axis and $1/d^2$ on the x-axis. According to the inverse square law, the graph should show a linear relationship.

6. Conclusion: If the plotted data aligns with a straight line, it confirms the inverse square law holds true for the point source of light.