Question

Consider a 1 cd isotropic illuminance light source. Answer the following:

a.What is luminance of light 10 ft from the source?

b. How much total light falls on a 1 str patch that is 10 ft from this light?

Answer 1

Answer:

The luminance of light and the amount of light are $8.56\times10^{-3}\ cd/m^2$ and $0.1076\ lumens/m^2$.

Explanation:

Given that,

Illuminance of light = 1 cd

Solid angle = 1 str

(a). We need to calculate the luminance

The luminance is the luminance intensity per unit area

$L=\dfrac{luminance\ intensity}{Area}$

$L=\dfrac{1\ cd}{4\pr^2}$

$L=\dfrac{1}{4\pi\times(3.048)^2}$

$L=0.008565=8.56\times10^{-3}\ cd/m^2$

(b). We need to calculate the amount of the light

Using formula of luminous flux

The luminous flux is equal to the product of the luminance intensity  and solid angle.

$\phi=I\times\Omega$

Where,$\Omega$=solid angle

I = luminance intensity

Put the value into the formula

$\phi=1\ cd\times1\ str$

The area of a patch on a sphere which is substand by a solid angle $\Omega$

$A=\Omega r^2$

$A=1\times(3.048)^2$

$A=9.290304\ m^2$

We need to calculate the amount of light received by the surface

$B=\dfrac{\phi}{A}$

Where, $\phi$ = luminous flux

A= area

Put the value into the formula

$B=\dfrac{1}{9.290304}$

$B=0.1076\ lumens/m^2$

Hence, The luminance of light and the amount of light are $8.56\times10^{-3}\ cd/m^2$ and $0.1076\ lumens/m^2$.