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Lens Formula

fv and fr a...

Question

$f_{v}$ and $f_{r}$ are the focal lengths of a convex lens for violate and red light respectively and $F_{v}$ and $F_{r}$ are the focal lengths of a concave lens for voilet and red light respectively, then

f_{v} < f_{r}

and

F_{v} > f_{r}

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f_{v} < f_{R}

and

F_{v} < f_{r}

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f_{c} > f_{r}

and

F_{v} > f_{r}

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f_{v} > f_{r}

and

F_{v} < f_{r}

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Solution

The correct option is B $f_{v} < f_{R}$ and $F_{v} < f_{r}$
According to lens makers formula
$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{1} - 2}) \Rightarrow \frac{1}{f} \propto (μ - 1)$
Since $μ_{v i o l e t} \Rightarrow f_{v} < f_{r}$ and $F_{v} < F_{r}$
Always keep in mind that whenever you are asked to compare (greater than or less than) $ν, v o r f$ you must not apply sign conventions for comparison.

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Similar questions

f_{V}

f_{R}

F_{V}

F_{R}

f_{V}

f_{R}

(f_{r} - f_{v})

(f)

(ω)

f_{r} - f_{v} = ω f

f_{v} \to

f_{r} \to

f_{U V} \to

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