Question

An object is placed 200 cm in front of a concave mirror. The image appears in the exact same location, 200 cm in front of the mirror (on top of the object itself). What is the focal length of the mirror?
A. 50 cm
B. 100 cm
C. 200 cm
D. 400 cm

Answer 1

B. 100 cm
The object is located where the image is as well, so so=si. Substitute this into the equation sosi=f^2, and you'll get s^2o=f^2. This tells you that so is equal to f (focal length) when disregarding the negative. Therefore, the focal point has to be exactly halfway between the object (200cm) and the mirror (200cm).

Answer 2

Answer:

B. 100 cm

Explanation:

Using mirror equation; $\frac{1}{d_{i} } + \frac{1}{d_{o} }  = \frac{1}{f}$

(Please ignore the A cap, I don't know how it appeared here, It's not in the equation tool )

where $d_{i}$ is distance of image = 200 cm

$d_{o}$ is distance of object = 200 cm

and $f$ is focal point.

.......substituting for $d_{i}$ and $d_{o}$

$\frac{1}{200} + \frac{1}{200}  = \frac{1}{f}$

${2f} = {200}$

$f = 100 cm$