Question

Two lenses of powers +5D and –3D are placed in contact. Find (i) the focal length and (ii) the power of the combined lens.

Hint:

When lenses are in contact, their powers simply add algebraically.

Answer 1

Step 1: Formula of lens power.
Power of a lens: $P = \dfrac{100}{f \, (\text{cm})} = \dfrac{1}{f \, (\text{m})}$.
Step 2: Combined power of lenses in contact.
\[ P = P_1 + P_2 = +5D + (-3D) = +2D \]
Step 3: Combined focal length.
\[ f = \frac{1}{P} = \frac{1}{2} \, m = 0.5 \, m \]
Step 4: Conclusion.
The combined lens acts like a converging lens with $f = 0.5m$ and $P = 2D$.