# Concave mirror - finding object and image distance

phys62

## Homework Statement

A concave mirror has a focal length of 27.2 cm. The distance between an object and its image is 50.2 cm. Find (a) the object and (b) the image distance assuming that the object lies beyond the center of curvature.

## Homework Equations

f=1/2 R
1/object distance + 1/image distance = 1/f

## The Attempt at a Solution

image distance - object distance = 50.2 cm
(image distance + object distance)/(image distance*object distance) = 1/f
50.2/(image distance*object distance)=1/27.2
image distance*object distance=1365.44

image distance=50.2 + object distance

substitute in and get: (50.2 + object distance)object distance = 1365.44
quadratic equation solves for object distance = 69.77 or 19.57 cm

Am I even doing this right?? If so, I'm stuck from here.. Thanks for any help you can give!

Staff Emeritus
Homework Helper

## Homework Statement

A concave mirror has a focal length of 27.2 cm. The distance between an object and its image is 50.2 cm. Find (a) the object and (b) the image distance assuming that the object lies beyond the center of curvature.

## Homework Equations

f=1/2 R
1/object distance + 1/image distance = 1/f

## The Attempt at a Solution

image distance - object distance = 50.2 cm
(image distance + object distance)/(image distance*object distance) = 1/f
Whoops.
image distance - object distance = 50.2 cm
But you substituted 50.2 cm for image distance + object distance

Try substituting for "image distance" in
1/object distance + 1/image distance = 1/f​

phys62
Can anyone help me figure out if I'm even on the right track?

phys62
so I tried saying image distance = 50.2 + object distance

substituting that into 1/object distance + 1/image distance = 1/f

I got object distance = -620.65 cm
then image distance would = -620.65 + 50.2 = -570.45 cm

This is incorrect... Have I done this right, and the 620.65 simply needs to be positive? Or am I completely off track?

Staff Emeritus