Question

A convex lens of power + 6D is placed in contact with a concave lens of power - 4 D. What is the nature and focal length of the combination- 

1. Concave, 25 cm
2. Convex, 50 cm
3. Concave, 20 cm
4. Convex, 100 cm

Answer 1

Correct Answer - Option 2 : Convex, 50 cm

Concept:

• Power of Lens (P): Power of Lens is the reciprocal of focal length (f). 

\(P = \frac{1}{f}\)

• Unit of Power of Lens is diopter (D).
• When two or more lenses are kept in Contact, then the power of the combination of the lens is the sum of the Power of all lenses.

Power of n number of the lens in contact is given as

P = P1 + P2 + P3 + ... Pn

• Power and focal length of the concave lens are negative.
• Power and focal length of the convex lens are positive.

Calculation:

Given

Power of Convex lens P₁ = + 6 D

Power of Concave lens P₂ = - 4 D

Net Power is the sum of the power of all lens

P = P1 + P2

⇒ P = 6 D - 4 D = 2 D

So, Power of Combination is 2 D

Focal length \(f = \frac{1}{P}\)

\(\implies f = \frac{1}{2} = 0.5m\)

focal length = 0.5 m = 50 cm

The sign is positive, therefore the combination of the lens is convex in nature.

So, Convex lens with 50 cm focal length is the correct answer.