First slide

The lens

Question

$f_{v} and f_{r}$ 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

Moderate

A

$f_{v} < f_{r} and F_{v} > F_{r}$
B

$f_{v} < f_{R} and F_{v} < F_{r}$
C

$f_{v} > f_{r} and F_{v} > F_{r}$
D

$f_{v} > f_{r} and F_{v} < F_{r}$

Solution

According to lens makers formula
$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) \Rightarrow \frac{1}{f} \propto (μ - 1)$
$since μ_{Red} < μ_{violet} \Rightarrow f_{v} < f_{r} and F_{v} < F_{r}$
Always keep in mind that whenever you are asked to compare (greater than or less than) u, v or f you must not apply sign conventions for comparison

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