Question

A convex lens of power +5D is placed in contact with concave lens of power −1.5D. Answer the following questions:

1. What is combined power of lens system?
2. What is the focal length of this system?
3. Can this combination can be used as a simple microscope?

Answer 1

Power of convex lens (P₁) = +5 D

Power of concave lens (P₂) = −1.5 D

(i) Applying, P = P₁ + P₂

= +5 + (−1.5)

= +3.5 D

Thus, the combined power of the lens system is +3.5 D.

(ii) Applying, \[ \mathrm{P} = \frac{100}{f \text{(in cm)}} \]

\[ \Rightarrow 3.5 = \frac{100}{f \text{(in cm)}} \]

\[ \Rightarrow f = \frac{100}{3.5} \]

\[ \therefore \ f = + \ 28.57 \ \text{cm} \]

Thus, the focal length of the system is 28.57 cm.

(iii) Yes. As the combined power is positive (+3.5 D), the combination behaves as a convex (converging) lens. Hence it can be used as a simple microscope.