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The focal length of a lens of dispersive power 0.45 which should be placed in contact with a convex lens of focal length $84 \mathrm{~cm}$ and dispersive power 0.21 to make the achromatic combination from the two lenses, in $\mathrm{cm}$ is
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The correct answer is:
-180
Here, $\quad \omega_1=0.45$
$\omega_2=0.21$ and $f_2=84 \mathrm{~cm}$
As the lens are kept is contact it is achromatic condition.
$\begin{aligned}
\therefore \quad \frac{\omega_1}{\omega_2} & =-\frac{f_1}{f_2} \\
\frac{0.45}{0.21} & =-\frac{f_1}{84} \\
\Rightarrow \quad f_1=-\frac{45 \times 84}{21} & =-180 \mathrm{~cm}
\end{aligned}$
$\omega_2=0.21$ and $f_2=84 \mathrm{~cm}$
As the lens are kept is contact it is achromatic condition.
$\begin{aligned}
\therefore \quad \frac{\omega_1}{\omega_2} & =-\frac{f_1}{f_2} \\
\frac{0.45}{0.21} & =-\frac{f_1}{84} \\
\Rightarrow \quad f_1=-\frac{45 \times 84}{21} & =-180 \mathrm{~cm}
\end{aligned}$
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