A point source of light is 8.00 m away from a surface - Scottish Highers Physics - Question 15 - 2017

To calculate the new irradiance when the distance of the point source from the surface changes, we use the inverse square law of light, which states:

$I = \frac{P}{4 \pi r^2}$

where:

• $I$ is the irradiance,
• $P$ is the power of the source (which we can derive from the original irradiance and distance), and
• $r$ is the distance from the light source to the surface.

1. Calculate the original power (P): We can rearrange the formula: $P = I \times 4 \pi r^2$ Plugging in the known values (for original conditions):

   • $I = 50.0 \, \text{mW m}^{-2}$,
   • $r = 8.00 \, \text{m}$: $P = 50.0 \, \text{mW m}^{-2} \times 4 \pi (8.00 \, ext{m})^2$

2. Calculate the new irradiance at the new distance (12.0 m):

   • Using the same power $P$ calculated from above and the new distance $r = 12.0 \, \text{m}$: $I_{new} = \frac{P}{4 \pi (12.0 \, ext{m})^2}$

3. Substituting back: After calculating both steps appropriately, we find that: The new irradiance $I_{new}$ results in 22.2 mW m^-2.