Question

A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25cm. The power of the combination in diopters is:
A. -1.5
B. -6.5
C. +6.5
D. +6.67

Answer 1

Given

• There are two lenses in contact
• Focal length of convex lens = 40 cm
• Focal length of concave lens = -25 cm

To Find

• Power of the combination

Solution

● We know that power of the combination will be given by, P = P₁ + P₂

● Power of each lens will be given by, P = 100/f

✭ Power of Convex Lens

→ P = 100/f

→ P = 100/40

→ P₁ = 2.5

✭ Power of Concave Lens

→ P = 100/f

→ P = 100/-25

→ P₂ = -4

━━━━━━━━━━━━━━━━━━

✭ Power of the Combination

→ P = P₁ + P₂

→ P = 2.5 + (-4)

→ P = 2.5 - 4

→ P (Combination) = -1.5 D

∴ The answer to the Question is Option A

Answer 2

Given :

Focal length of a convex lens (f1) = 40 cm = 0.4 m and

Focal length of a concave lens (f2) = - 25 cm = - 0.25 m (minus sign due to concave lens).

To Find :

Power of the combination

Solution :

(f1) = 40 cm = 0.4m , (f2) = - 25 cm = -0.25m

→ 1/f = 100/f₁ + 100/f₂

→ 1/f = 100/40 + 100/-25

→ 1/f = 2.5 + -4

→ 1/f = -1.5

━━━━━━━━━━━━━━━

★ Power of the combination = -1.5 D

So the correct answer is Option A