Question

suppose an isotropic light source has a power of 58 w and that its light is normally incident on a partially-reflecting surface at a distance of 4.91 m from the source. calculate the average radiation pressure (in npa) if the surface reflects 29% of the incident light. (Use c = 2.9979 × 10⁸ m/s)

Answer 1

The average radiation pressure on a partially-reflecting surface by an isotropic light source is calculated using the light intensity at the surface and accounting for the percentage of light reflected. The radiation pressure formula considers both the absorbed and reflected light components to provide the final pressure in Pascals.

Step-by-step explanation:

To calculate the average radiation pressure exerted by an isotropic light source on a partially reflecting surface, we can use the formula for radiation pressure P = I/c, where I is the intensity of the light and c is the speed of light. The intensity I can be found using I = P/A, where P is the power of the light source and A is the area over which the power is spread. Since the surface reflects 29% of the incident light, this factor must be included in the final calculation of the reflected radiation pressure.

First, calculate the surface area A of a sphere with a radius equal to the distance from the light source to the surface (A = 4r^2). Then compute the intensity I at that distance. The radiation pressure for total absorption is P = I/c, but since the surface is partially reflecting, we have two components: the absorbed part and the reflected part. For the reflected part, the pressure is doubled, so the average radiation pressure is P_avg = I(1 + R)/c, where R is the reflectance (0.29 in this case).

Using the given values, the intensity I at 4.91 m is calculated and then used to compute the average radiation pressure on the reflecting surface in Newtons per square meter (N/m²), which can also be expressed in Pascals (Pa), since 1 N/m² = 1 Pa.