A 76-cd point source of light is 3.2 m above the surface of a desk. What is the illumination on the desk's surface in lux?

To calculate the illumination on the desk's surface, we can use the inverse square law for light intensity. According to this law, the intensity of light decreases as the square of the distance from the light source increases.

The formula to calculate the illumination (I) in lux is given by:

I = (L * A) / d^2

Where:
L is the luminous intensity (in candela) of the light source
A is the area (in square meters) on which the light is falling
d is the distance (in meters) between the light source and the surface

In this case, the formula becomes:

I = (L * A) / (3.2^2)

Since the luminous intensity of the light source is given as 76 cd, and we need to find the illumination on the desk's surface, we only need to determine the area on which the light is falling.

Assuming the light source emits light in all directions equally, we can consider a sphere around the source and calculate the area of the sphere on which the light is falling. The formula for the surface area of a sphere is 4πr^2, where r is the radius of the sphere.

In this case, the radius of the sphere is 3.2 m because the light source is 3.2 m above the surface of the desk. So, the surface area of the sphere is:

A = 4π * (3.2)^2

Now we can plug the values into the formula for illumination:

I = (76 * [4π * (3.2)^2]) / (3.2^2)

Simplifying the expression:

I = 76 * 4π

Calculating the value:

I ≈ 301.592894

Therefore, the illumination on the desk's surface is approximately 301.6 lux.

To find the illumination on the desk's surface in lux, we need to use the inverse square law of light. According to the inverse square law, the intensity of light decreases as the square of the distance from the source increases.

First, we need to find the intensity of the light at the desk's surface. We know that the light source is a point source, and the intensity of a point source of light is defined as the power emitted per unit solid angle. However, in this case, we have 76-cd (candela), which is a unit of luminous intensity.

Since luminous intensity refers to the energy emitted in a particular direction, we need to determine how much of that energy hits the desk's surface. To do this, we need to calculate the solid angle subtended by the desk as seen from the light source.

Using the formula for solid angle (Ω = A/r^2), we can calculate the solid angle (Ω) subtended by the desk. Here, A represents the area of the desk, and r represents the distance from the desk to the light source. Since the light source is a point source, we can assume that the area (A) is negligible, and we only need to consider the distance (r).

Given that the light source is 3.2 m above the surface of the desk, the distance (r) is also 3.2 m. Thus, Ω = A/r^2 = A/3.2^2.

Now, we need to convert the luminous intensity (cd) to the radiant intensity (W/sr). The conversion for this is 1 cd = 1 lm/sr, where lm represents luminous flux.

Since we have 76 cd, the radiant intensity is equal to 76 lm/sr.

Finally, to find the illuminance (E) on the desk's surface in lux, we need to multiply the radiant intensity by the solid angle subtended by the desk (Ω), and divide by the area (A) of the desk.

E = (radiant intensity * Ω) / A.

Since the area (A) is negligible, we can assume it to be 1. Therefore, the illuminance (E) on the desk's surface in lux is equal to the radiant intensity (76 lm/sr) multiplied by the solid angle, which is equal to π (since it's a point source), divided by 3.2^2 (since the light source is 3.2 m away from the desk).

E = (76 lm/sr * π) / (3.2^2) lux ≈ 2.981 lux.

Therefore, the illumination on the desk's surface is approximately 2.981 lux.