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

• bnwchbammer
In summary, a Candela (cd) is a unit of measurement for luminous intensity, measuring the amount of light emitted in a specific direction. It is different from a Watt (W), which measures power, and its brightness decreases with distance. A Candela can be converted to other units such as Lumens (lm) or Foot-candles (fc). Light bulbs are usually measured in Lumens, not Candelas.
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.

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

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.

## 1. What is a Candela?

A Candela (cd) is the standard unit of measurement for luminous intensity, which is the amount of light emitted in a particular direction from a light source.

## 2. How is a Candela different from a Watt?

A Watt (W) is a unit of power, which measures the amount of energy consumed or produced over time. A Candela, on the other hand, measures the brightness or intensity of light emitted in a specific direction.

## 3. How does distance affect the brightness of a Candela?

The brightness of a Candela decreases as distance from the light source increases. This is due to the spreading out of light rays over a larger area, resulting in a lower intensity at greater distances.

## 4. Can a Candela be converted to other units of measurement?

Yes, a Candela can be converted to other units of measurement such as Lumens (lm) or Foot-candles (fc). Lumens measure the total amount of light emitted from a source, while Foot-candles measure the amount of light that falls on a given area.

## 5. How is the brightness of a light bulb measured in Candelas?

The brightness of a light bulb is not typically measured in Candelas, as it is a unit more commonly used for directional light sources. Light bulbs are usually measured in Lumens, which takes into account the total amount of light emitted in all directions.

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