Clarification regarding the use of Lambert's Cosine Law

[misterlimbo]

Homework Statement

A light bulb is used to light a bunker 10 feet below. A chair sits on the floor of the bunker 3 feet from a spot directly below the bulb. What is the illumination on the floor around the chair if the luminous intensity is 150 candles?

Homework Equations

* Lambert's Cosine Law: E(θ) = Ecosθ
where E is the illumination (illuminance) measured at a point "normal" to the source

* E = luminous flux / area = F / A

* luminous flux intensity, I = luminous flux / solid angle = F / Ω

The Attempt at a Solution

I = F / Ω
I = 150 cd
Ω = 4*pi = 4π steradians
--> F = 600π lumens

E = F / A
E = 600π / [4π*((10² +3²)^.5)²]
--> E = 150/109 lm/ft² =1.376 lm/ft²

E(θ) = Ecosθ
E(θ) = Ecos(tan^-1(3/10))
--> E(θ) = 1.318 lm/ft²

* My question is, did I use the right distance? That is, to use the direct distance from the light source to the chair (which was obtained through Pythagorean theorem) and not just 10ft?

Thanks in advance

 

[KataKoniK]

for your help!

it is important to accurately represent the physical situation in your calculations. In this case, it is more appropriate to use the direct distance from the light source to the chair, rather than just the depth of the bunker. This is because the light is directly illuminating the chair, and the distance between the light and the chair will affect the amount of illumination received.

Therefore, your calculation using the Pythagorean theorem to find the direct distance of 10.44 feet is correct. This should be used in your calculation for the illumination at the chair's location. Keep up the good work!