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

The luminance of light and the amount of light are
`8.56*10^(-3)\ cd/m^2` and
`0.1076\ lumens/m^2`.

Step-by-step 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=(luminance\ intensity)/(Area)`

`L=(1\ cd)/(4\pr^2)`

`L=(1)/(4\pi*(3.048)^2)`

`L=0.008565=8.56*10^(-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*\Omega`

Where,
`\Omega`=solid angle

I = luminance intensity

Put the value into the formula

`\phi=1\ cd*1\ str`

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

`A=\Omega r^2`

`A=1*(3.048)^2`

`A=9.290304\ m^2`

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

`B=(\phi)/(A)`

Where,
`\phi` = luminous flux

A= area

Put the value into the formula

`B=(1)/(9.290304)`

`B=0.1076\ lumens/m^2`

Hence, The luminance of light and the amount of light are
`8.56*10^(-3)\ cd/m^2` and
`0.1076\ lumens/m^2`.