Question

A parallel beam of monochromatic light falls on a combination of a convex lens and a concave lens of focal lengths 15 cm and 5 cm respectively.What is the distance between the two lenses to obtain a parallel beam of light from the concave lens?
options are :
a) 20 cm b) 3 cm c) 10 cm d) 45 cm

Answer 1

Answer on Question 38958, Physics, Optics We will use formula for 2-lens system here. The effective focal length of such system is

$\frac{1}{f_{eff}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{l}{f_{1}f_{2}}$

$f_{eff}=\frac{1}{\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{l}{f_{1}f_{2}}}$

where $f_{1}$, $f_{2}$ are focal lengthes of the 1 and lens and $l$ is distance between them. For concave lens $f_{2}$ should be negative.

We need $f_{eff}$ to be infinity if we want to keep parallel beam parallel. Hence, equation for distance $l$ is

$\frac{1}{f_{1}}+\frac{1}{f_{2}}-\frac{l}{f_{1}f_{2}}=0$

$l=\left(\frac{1}{f_{1}}+\frac{1}{f_{2}}\right)f_{1}f_{2}$

$l=-\left(\frac{1}{15}-\frac{1}{5}\right)\cdot 15\cdot 5=10\,cm$

Hence, answer is c) 10 cm.