Question: You are given three lenses L1, L2 and L3 each of focal length 15cm. An object is kept at 20 cm in fr...

Question

You are given three lenses L1, L2 and L3 each of focal length 15cm. An object is kept at 20 cm in front of L1, as shown. The final real image is formed at the focus 'I' of L3. Find the separations between L1, L2 and L3.

Answer 1

Solution

Hint: The rays reflected and pass through a common point on the principal axis is called a focal point. Use a lens formula to calculate the distance between lenses by using object and image distance. Lens equation gives a quantitative relation between image distance, object distance and focal length.

Complete step-by-step answer:
Question explanation- We have given three lenses L1, L2, L3 and each having each of focal length is 15cm. an object is placed 40cm away from L1. The real image formed after L3 at 15cm. find the distance between L1, L2 and L3.
Aim: Find the separations between L1, L2 and L3.
We have focal length f=15cm
u= object distance from lens L1 which is 15cm
v= image distance from L3 which is 20cm
Then according to sign convention, sign on the left side of the lens is positive and sign on right is negative.
Using Lens formula,
$\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}$
Rearrange above equation, we get
$\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}$
$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{-20}=\dfrac{1}{60}$
$v=60cm$
Here, the image by L3 is at a distance 15cm means at the focus. So objects must lie at infinity for L3.
Therefore we can say that objects forL2 should be at focus.
So the distance between L1 and L2 is 60+15=75cm.
X1=75cm
The question stated that the final real image is formed at the focus 'I' of L3.
So the distance between L2 and L3 can be anything because the image must be at focus. So the distance between L2 and L3 can be any value.

Note: Generally u stands for object distance from the given lens and v stands for image distance from the given lens. Do not get confused between the lens formula and mirror formula. Difference between these two formulae is just a sign. So be careful. Lens and mirrors are different. The lens is an optical device that is used to focus the light at desired distance.