How Far Should the 70-cd Lamp Be to Match the 10-cd Lamp's Intensity?

[bnwchbammer]

Homework Statement

A 10-cd point source lamp and a 70-cd point source lamp cast equal intensities on a wall. If the 10-cd lamp is 8.0 m from the wall, how far from the wall is the 70-cd lamp?

Homework Equations

I'm not sure what the equation for a candela is.

The Attempt at a Solution

Can't attempt it without knowing an equation.


That's the only information given, and I don't know how to form an equation.

 

[nickjer]

A candela is a unit of intensity for light. And you remember that intensity falls off as 1/r^2.

 

[nlightner]

As a scientist, it is important to always have access to reliable information and to use appropriate equations to solve problems. In this case, the equation for finding the intensity of light is I = P/A, where I is intensity, P is power, and A is the area. For a point source lamp, the area can be approximated as a sphere, so the equation becomes I = P/4πr^2, where r is the distance from the lamp to the surface it is illuminating.

Using this equation, we can solve for the distance of the 70-cd lamp by setting the intensity of both lamps equal to each other and solving for r:

I1 = I2
P1/4πr1^2 = P2/4πr2^2
10/4π(8.0)^2 = 70/4πr2^2
r2 = √[(10/70)(8.0)^2]
r2 ≈ 3.2 m

Therefore, the 70-cd lamp should be placed approximately 3.2 m from the wall in order to produce the same intensity as the 10-cd lamp at a distance of 8.0 m. It is important to note that this is an approximation and may vary depending on the exact size and shape of the lamps.