Question

A convex lens is made of glass (n = 1.5) with one flat surface and the other surface being convex
having a radius of 40 cm.

a. What is the focal length of the lens?
b. How far in front of the lens must a 10 cm high object be placed such that the image produced is
virtual and 30 cm high?

Answer 1

Solution:-

let,

R1=Radius of the flat surface

R2= Radius of the convex surface

f=Focal length

h1=height of the object

h2=height of the image

v=image distance

u=object distance

m=magnification

Given,

n (refractive index)= 1.5

R2=-40cm

R1=infinity

h=10cm

h2=30cm

for flat surface radius is infinity

R2 is negative because of the convex surface

a) we know that the lens maker formula is-

1/f=(n-1)(1/R1-1/R2)

1/f = (1.5-1)(0+1/40) (since 1/infinity =0)

1/f=0.5/40

f=40/0.5

f=80 cm

Focal length is 80 cm

b) we know that,

m=h2/h1

f/f+u=h2/h1

80/(80+u)=30/10

30(80+u)=800

2400+30u=800

30u=800-2400

u=-1600/30

u=-53.3 cm

Therefore image should be placed 53.3 cm in front of the lens.