Question

You place an object 28.23 cm in front of a diverging lens which has a focal length with a magnitude of 12.54 cm, but the image formed is larger than you want it to be. Determine how far in front of the lens the object should be placed in order to produce an image that is reduced by a factor of 3.1.

Answer 1

We know that the magnification of the lens

M=-i/o. ..1

Now using lens equation

1/f=1/i+1/o

1/i=1/f-1/o

Here f=-12.54 cm , o=28.23 cm

1/i=-1/12.54 -1/28.23

1/i=(-28.23-12.54)/(12.54×28.23)

i=-12.54×28.23/(40.77)

i=-8.68 cm

So from equation 1

M=-(-8.68)/28.23

M=0.308

For new location

M'=-i'/o'

According to the Question M'=0.308/3.1 =0.0994

So

i' =-0.0994 o

Again Using lens equation

1/f=1/i'+1/o'

1/f =-1/0.0994o' +1/o'

1/f =(1/0.0994o')(-1+0.0994)

1/f=-0.9006/o'

o' =-0.9006f

o' =-0.9006×(-12.54)

o'=11.293554 cm

o' =11.29 cm. Answer