Question

Two lenses of focal lengths 20 cm and -40 cm are held in contact. The image of object at infinity will be formed by the combination at
A. 10 cm
B. 20 cm
C. 40 cm
D. infinity

Answer 1

Hint: In this question we are asked to calculate the image distance formed by the combination of two given lenses. To solve this question, we shall first calculate the equivalent focal length of the combination. It is given that the object is placed at infinity. Therefore, using the lens formula, we shall calculate the image distance.
Formula Used: $${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{f_1}}+{\displaystyle \frac{1}{f_2}}$$
f is the equivalent focal length
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$$
Where,
v is the image distance
u is the object distance
f is the focal length

Step by Step Solution:
We know that for a combination of lenses the equivalent focal length is given by,
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{f_1}}+{\displaystyle \frac{1}{f_2}}$$
After substituting the given values,
We get,
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{20}}+{\displaystyle \frac{1}{(-40)}}$$
Therefore,
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{2-1}{40}}$$
Therefore,
$$f=40cm$$
Now using lens formula,
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$$
It is given that object is at infinity
Therefore,
$${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}$$
Therefore,
$$f=v=40cm$$
Therefore, the image distance of the image formed by the given combination of lens is 40 cm.

Therefore, the correct answer is option C.

Note:
Focal length of the lens is the distance from the centre of the lens to the principal foci of the lens. The focal length of the lens is a defining parameter of the lens. Focal length can change the perspective and scale of the image that is formed. The degree of convergence or divergence of the light rays falling on the lens is known as power of the lens.