Question

A concave mirror with a focal length of 43 cm produces an image whose distance from the mirror is one-fifth the object distance. Find the object and image distances.

Object: __________ cm

Image: __________ cm

**Please explain/show all work so I may do problems like this in the future. Will rate! Thank you!**

Answer 1

1/f = 1/v + 1/u

Hence, 1/43 = 5/u + 1/u

Hence, u=43x6 cm = 258 cm

image distance = v = u/5 = 258/5 = 51.6 cm

Answer 2

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A concave mirror with a focal length of 37 cm produces an image whose distance from themirror is one-half the object distance. Find the objectand image distances.

object	cm
image	cm

answer

Given

   focal length f = 37 cm

   image whose distance from the mirror isone-half the object distance

image distance v = u /2

--------------------------------------------------------------

      ( 1 / f) = ( 1 / u ) +(1/ v)

    ( 1/f ) = (1/ u) + ( 2 / u)

  

      u = 3f

   object distance u = 111cm

  

   image distance v = 55.5cm

Answer 3

The formula that relates focal length (f), object distance (o) and image distance (i) is

1/f = 1/o + 1/i
or f =o*i/o+i
since the distance of the image is half that of the object distance it can be written as i = o/5 or o= 5*i.
Expressing o in terms of i and substituting in the equation for f, we get
f = 5*i*i/5i+i
f =5i/6
since f is given as 43 cm
i = 43*5/6 = 35.83 cm
o = 5*35.83 = 179.15 cm