Question

An achromatic combination of concave and convex lens has power $5$D. If the power of convex lens is $4$D, then the magnitude of focal length of concave lens is?

Answer 1

Let power of concave lens and convex lens be $P_1\&P_2$ respectively.

( here $P_2$ is (+)ve & $P_1$ is (-)ve.

$\Rightarrow P_1=?,$ $P_2=+4D,$ $P_1+P_2=5D$ $P_1=1D$

but power of concave lens, $P_1=-1D$

$\Rightarrow P\alpha \frac{1}{f}$

$\Rightarrow \frac{1}{f_1}=+1D$

$\Rightarrow f_1=+1m$

Mean force path, ${\lambda }_{+}=\frac{kT}{\sqrt{2}\pi P{d}^2}$

i.e, $\lambda \alpha T$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{T_1}{T_2}=\frac{150}{300}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=0.5$

Hence, the answer is $\mathrm{0.5.}$