An object is placed 25cm in front of a convex mirror has its image formed 5cm behind the mirror. what is the focal length of the convex mirror

An object is placed 25cm in front of a convex mirror has its image formed 5cm behind the mirror. what is the focal length of the convex mirror

Answer Details

Object distance (u) = -25 cm (negative because the object is in front of the mirror)
Image distance (v) = +5 cm (positive because the image is behind the convex mirror)

Using  1f $\frac{1}{f}$ = 1u $\frac{1}{u}$ + 1v $\frac{1}{v}$

1f $\frac{1}{f}$ = 1−25 $\frac{1}{-25}$ + 15 $\frac{1}{5}$

f = 254 $\frac{25}{4}$ = 6.250cm.