Question

A convex lens of power $+6$ dioptre is placed in contact with a concave lens of power $-4$ dioptres. What will be the nature and focal length of this combination?

• A. Concave, $25cm$
• B. Convex, $50cm$
• C. Concave, $20cm$
• D. Convex, $100cm$

Answer 1

The correct option is B Convex, $50cm$

Let the focal length of the convex lens be $f_1$ and that of concave lens be $f_2$.

Given : power of convex lens , $P_1=+6dioptre$

power of concave lens , $P_2=-4dioptre$

Using $poweroflens=\frac{1}{focallength\left(f\right)}$ where $f$ is in metre

Let focal length of the combination be $F$

now $\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

$\frac{1}{F}=6+(-4)$

thus $F=50cm$

As $F$ comes out to be positive, hence the combination of the two lenses is a convex lens.