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BITSAT 2022 Paper

Section: Physics

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Question : 30 of 130

Marks: +1, -0

An achromatic convergent doublet of two lenses in contact has a power of

+5 D

. The power of converging lens is

+6 D

. The ratio of the dispersive power of the convergent and divergent lenses is

$3: 7$
$2: 3$
$1: 5$
$5: 3$

Solution: 👈: Video Solution

The condition of achromatism is

W_1P_1 + W_2P_2 = 0

\Rightarrow W_1P_1 = - W_2P_2

\frac{W_1}{W_2} = \frac{P_2}{P_1} .......... (i)

Now,

P_1 + P_2 = 4D .......... (ii)

but, Power of converting lens,

P_1 = 5D

∵ Power of diverging lens

P_2 = 4D - P_1

[From ii]

= 4D - 5D = -D

∴ From Eq. (i), we have

\frac{W_1}{W_2} = \frac{P_2}{P_1} = \frac{-(-D)}{5D} = \frac{1}{5} \Rightarrow \frac{W_1}{W_2} = \frac{1}{5}

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