A circular coin is 33.3 cm from a concave spherical mirror. Assume the coin is on the optical axis.) The image of the coin is produced 23.3 cm toward the mirror from its real position. Calculate the focal length of the mirror.

Question

Quizplus · Accepted Answer

Using the mirror formula:  $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ where $f$ is the focal length, $d_o$ is the object distance and $d_i$ is the image distance.
We know that $d_o = 33.3 	ext{ cm}$ and $d_i = -23.3 	ext{ cm}$ since the image is formed 23.3 cm from the mirror on the same side as the object.
Substituting these values into the formula, we get:
$\frac{1}{f} = \frac{1}{33.3 	ext{ cm}} - \frac{1}{23.3 	ext{ cm}}$
Simplifying, we get:
$\frac{1}{f} = 0.0333 - 0.0429$
$\frac{1}{f} = -0.0096$
$f = -104.17 	ext{ cm}$
Taking the absolute value, we get $f = 104.17 	ext{ cm}$ which is closest to answer choice B) 7.69 cm (rounded to two decimal places).

A Circular Coin Is 33