Question

A concave lens has focal length 15 cm. At what distance should the object from the lens should be placed so that it forms an image at 10 cm from the lens? Also find the magnification produced by the lens.

Answer 1

Step 1, Given data

Focal length, f = -15 cm after sign conventions

Image distance, v = -10 cm

Object distance = ?
Step 2, Finding the object distance and magnification

From the lens formula:

We know,

$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$

$\frac{1}{u}$ = $\frac{1}{v}$ - $\frac{1}{f}$

$\frac{1}{u}$ = $\frac{-1}{10}$ + $\frac{1}{15}$

= $\frac{-3+2}{30}$

= $\frac{-1}{30}$

Therefore,

u = -30 cm

Now,

We know,

Magnification= m = $\frac{v}{u}$

m = $\frac{-10}{-30}$

m = $\frac{1}{3}$

m = 0.33(Positive)

Thus the image is virtual, erect and diminished.

Hence,

The object distance = $30cm$

Magnification = $\frac{1}{3}=0.33$