Q147 / 160 · AP EAMCET 2011 · Physics

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

  • A
    45
  • B
    90
  • C
    180
  • Correct answer
    D
    -180

Solution

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. $\begin{aligned} \therefore \quad \frac{\omega_1}{\omega_2} & =-\frac{f_1}{f_2} \\ \frac{0.45}{0.21} & =-\frac{f_1}{84} \\ \Rightarrow \quad f_1=-\frac{45 \times 84}{21} & =-180 \mathrm{~cm} \end{aligned}$

Hence, the correct answer is option: 'D'.

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