Example from Physics, 16.1 Reflection

Calculating Object Distance

Electric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR radiation follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0 cm and produces an image of the coils 3.00 m in front of the mirror, where are the coils with respect to the mirror?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We are told that the concave mirror projects a real image of the coils at an image distance d_i = 3.00 m. The coils are the object, and we are asked to find their location—that is, to find the object distance d_o. We are also given the radius of curvature of the mirror, so that its focal length is f = R/2 = 25.0 cm (a positive value, because the mirror is concave, or converging). We can use the lens/mirror equation to solve this problem.
Solution
Because d_i and f are known, the lens/mirror equation can be used to find d_o.

$\frac{1}{f} = \frac{1}{d_{i}} + \frac{1}{d_{o}}$
16.1

Rearranging to solve for d_o, we have

$d_{o} = \frac{d_{i} f}{d_{i} - f} .$
16.2

Entering the known quantities gives us

$d_{o} = \frac{(3.00 \times 10^{2}) (25.0)}{(3.00 \times 10^{2}) - 25.0} = 27.3 cm .$
16.3

0 of 2 steps open

How did it go?

Strategy

Solution

Strategy

Solution