Question

An object is placed at a distance of 30 cm from a convex mirror, the magnification produced is 1/2. Where should the ohect be placed to get a magnificationof 1/3

Answer 1

In first case when magnification is 1/2

v/u=1/2

u=2v

From mirror formula

1/30+1/60=1/f

f=20cm

Thus focal length =20cm

In second case.

v/u=1/3

u=3v

From mirrors formula

1/3v+1/v=1/20

4/3v=1/20

v=80/3cm

Thus u=3v

=3*80/3

u=30cm

Answer 2

Answer is in the attachment.

◆ It is given that the object distance is 30 cm in front of the convex mirror and magnification produced is

$\frac{1}{2}$

◆ So using magnification we found the image distance which is 15cm.

◆ Now, by using mirror formula we found the focal length as 30cm.

◆ Next it is given that the new magnification is

$\frac{1}{3}$

so, we replace the value of 'v' in terms of 'u'.

◆ The focal length remains the same.

◆ Now, again using the mirror formula and by putting the value of focal length we found the object distance 'u' as 60cm.

$\boxed{answer \: \implies \: - 60cm}$