Q. $f_{v}$ and $f_{r}$ are the focal lengths of a convex lens for violet and red light respectively and $F_{v}$ and $F_{r}$ are the focal lengths of a concave lens for violet and red light respectively, then
A) $f_{v} < f_{r}$ and $F_{v} > F_{r}$
B) $f_{v} < f_{R}$ and $F_{v}$ < $F_{r}$
C) $f_{c} > f_{r}$ and $F_{v} > F_{r}$
D) $f_{v} > f_{r}$ and $F_{v} < F_{r}$
Explanation
(b) According to lens makers formula
$\frac{1}{f} = (\mu - 1)\left( \frac{1}{R_{1}} - \frac{1}{R_{2}} \right) \Rightarrow \frac{1}{f} \propto (\mu - 1)$
Since $\mu_{Red} < \mu_{violet} \Rightarrow f_{v} < f_{r}$ and $F_{v} < F_{r}$
Note: Always keep in mind that whenever you are asked to compared (greater than or less than) $u,\ v$ or $f$ you must not apply sign conventions for comparison
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.