Question

Find the magnification produced by a convex mirror of focal length 20 cm, if the object is kept at a distance of 15 cm from the mirror?​

Answer 1

Convention: the focal length of a convex mirror is negative. Using the mirror equation we get: - 1/15 = 1/20 + 1/Di

Di = - 60/7 cm = approx. - 8.57 cm. This is acceptable, because all images produced by convex mirrors are virtual, hence NEGATIVE and they are all diminished, as it is obviously in this case (Di < Do).

solved Example

A 4.0-cm tall light bulb is placed a distance of 35.5 cm from a convex mirror having a focal length of -12.2 cm. Determine the image distance and the image size.

 

Like all problems in physics, begin by the identification of the known information.

ho = 4.0 cmdo = 35.5 cmf = -12.2 cm

Next identify the unknown quantities that you wish to solve for.

di = ???hi = ???

To determine the image distance (di), the mirror equation will have to be used. The following lines represent the solution to the image distance; substitutions and algebraic steps are shown.

1/f = 1/do + 1/di

1/(-12.2 cm) = 1/(35.5 cm) + 1/di

-0.0820 cm-1 = 0.0282 cm-1 + 1/di

-0.110 cm-1 = 1/di

di = -9.08 cm

$\huge\rm\pink{HOPES}$ $\huge\rm\red{HELPS}$ $\huge\rm\orange{YOU}$