Question

One half of a convex lens of focal length 10cm is covered with black paper. Can such a lens produce an image of a complete object placed at a distance of 30cm from the lens ? Draw a ray diagram to justify your answer. A 4cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20cm. The distance of the distance of the object from the lens is 15cm. Find the nature, position and size of the image.

Answer 1

1.A convex lens can produce the complete image of the object even though half of the lens is covered .
Because light rays coming from the object can be refracted from the other part of the lens.

Refer the attachment for ray diagram.

2.Given:
 height of object= 4cm=h0
focal length=f=20cm.
u=-15cm after sign conventions.
by lens formula,
1/f=1/v-1/u
1/v=1/f+1/u=1/20-1/15=3-4/60=-1/60
v=-60cms
m=v/u
m=hi/ho=v/u
hi=hoxv/u
=4x(-60)/(-15)=8cm
hi=8cm
∴ Position of image is 60cm in front of lens
size of image is 8cm
nature of image is virtual and erect.

Answer 2

height of object= 4cm=h0

focal length=f=20cm.

u=-15cm after sign conventions.

by lens formula,

1/f=1/v-1/u

1/v=1/f+1/u=1/20-1/15=3-4/60=-1/60

v=-60cms

m=v/u

m=hi/ho=v/u

hi=hoxv/u

=4x(-60)/(-15)=8cm

hi=8cm

∴ Position of image is 60cm in front of lens

size of image is 8cm

nature of image is virtual and erect.