Question

Two glass lenses with index of refraction 1.50 are ground such that the front of each lens is convex with radius 1.0 m, and the back of each lens is concave with radius 2.2 m. A 4 cm tall object is placed 4.5 m from the first lens, and the lenses are 3 m apart.

a) What is the focal length of each lens?

b) Where will the image from the first lens be?

c) Where will the final image be (using both lenses)?

d) What will the height of the final image be?

Answer 1

(a)

n = 1.5

R1 = +1 m

R2 = +2.2 m

As the lenses are identical, focal length of each lens is same,

(b)

using lens's equation for the first lens we can calculate position of image formed .

given : u = object distance = - 4.5 m (real object distance is negative by cartesian sign convention)

f = 11/3 m

lens's equation:

the +ive sign signifies that the image formed is real.

(c)

object distance for 2nd lens = u ' = 19.8 - 3 = +16.8 m.

f = 11/3 m

v' = image distance from 2nd lens.

using lens's equation for 2nd lens,

(d)

Magnification =

therefore,

height of final image =   .