Question

An object is 25.0 cm from the mirror, its height is 5.0 cm, and focal length is 8.0 cm. What is the distance from the image to the mirror? 0.085 cm 1.6 cm 9.8 cm 12 cm

Answer 1

The equation needed to solve the problem is
$\frac{1}{f} = \frac{1}{d_{o}} + \frac{1}{d_{i}}$
where
f = focal length, 8.0 cm
do = object distance, 25.0 cm
di = image distance

Therefore
$\frac{1}{8} = \frac{1}{25} + \frac{1}{d_{i}} \\ 0.125 = 0.04 + \frac{1}{d_{i}} \\ \frac{1}{d_{i}} =0.125-0.04=0.085\\d_{i}= \frac{1}{0.085} =11.765 \, cm$
The closest answer is 12 cm.

Answer: 12 cm

Answer 2

1.) Use the formula to solve - 
             1/f = 1/do + 1/di; Where f = focal length; 1/do + 1/di
             1/f = 1/do + di
            1/8 = 1/25 + 1/?
          .125 = .04 + 1/di
   .125 -.04 = 1/di (transferred .04 to the left side of the equation)
       .085/1 = 1/di
.085di/.085 = 1/.085 (multiplied both sides by di and divided both sides by .085)
               di = 11.76 or 12
2.) Therefore, 12 cm is the distance from the image to the mirror