First slide

The lens

Question

Two lenses have focal lengths $f_{1} and f_{2}$ and their dispersive powers are $ω_{1} and ω_{2}$ respectively. They will together form an achromatic combination if

Moderate

A

$ω_{1} f_{1} = ω_{2} f_{2}$
B

$ω_{1} f_{2} + ω_{2} f_{1} = 0$
C

$ω_{1} + f_{1} = ω_{2} + f_{2}$
D

$ω_{1} - f_{1} = ω_{2} - f_{2}$

Solution

For achromatic combination, $\frac{ω_{1}}{f_{1}} + \frac{ω_{2}}{f_{2}} = 0$
$\Rightarrow ω_{1} f_{2} + ω_{2} f_{1} = 0$

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