The image obtained with a convex lens is erect

cbse
ray-optics

#1

The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distances.


#2

Given f = + 20 cm
As, magnification, m = I/O = v/u
I = 4 x length of object
====> I/O =4
===> v/u = 4
===> v = 4u
Using lens formula, 1/f = 1/v - 1/u

1/f = 1/(-4u) - 1/(-u)

1/f = -1/4u + 1/u
or
1/20 = 4-1/4u = 3/4u

u = 20x3/4 = 15 cm

v = 4u = 15x4 = 60 cm
Distance of the object, u = 15 cm
Distance of the image, v = 60 cm

The image is on the same side of the object.