Question

A convex lens has a focal length of 10 cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of (a) 9.8 cm, (b) 10.2 cm from the lens.

Answer 1

Given :

f= 10cm

a) u= - 9.8 cm

from lens formula :

1/f=1/v-1/u

1/v=1/f+1/u

1/v=1/10 -1/9.8

=1/10-10/98

=98-100/980

=-2/980

v= -980/2= - 490cm

m=v/u

m=- 490/- 9.8 = +50

so Nature of image :

• Virtual, erect and magnified .

• Image is formed on the same side of object

b) u = - 10.2cm

1/f=1/v-1/u

1/v=1/f+1/u

1/v=1/10-1/10.2

=1/10 - 10/102

=102-100/1020

=2/1020

v=1020/2

v=510cm

m=v/u= 510/- 10.2 = - 5100/102 = -50

so nature of image :

• image is formed beyond C2

• Real

• inverted

• and magnified

Answer 2

f=10cm,u=9.8cm  

v=+ve,u=−ve

We know

1/f=1/v−1/u⇒110=1/v+19.8

1v=110−19.8=9.8−1098

1v=−0.298⇒v=−9802

v=−490

v=−ve , so image virtual and same side of the object