Embibe Experts Solutions for Exercise 1: Exercise

Ray diagram for two lenses kept at some distance given in the diagram, which of the following option is correct (f1,f2=focal length; d=distance between lenses)

The refractive index of material of a Plano-convex lens, if the radius of curvature of the plane surface $\left(R_1\right)$ is infinite while the radius of curvature of convex surface $\left(R_2\right)$ is $20 \mathrm{c}\mathrm{m}$ and focal length of the lens is $30 \mathrm{c}\mathrm{m}$, will be:

A biconvex lens made of glass (refractive index $1.5$) has two spherical surfaces having radii $20 cm$ and $30 cm$. Calculate its focal length.

A concave lens of focal length $20 \mathrm{cm}$ product an image half in size of the real object. The distance of the real object is

Is magnification positive for concave lens?
 

For two thin lenses kept in contact with each other, show that:

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

where the terms have their usual meaning.

How is focal length defined for a two lens system, separated by distance d?

When two thin lenses are kept in contact, prove that their combined or effective focal length F is given by:
$\frac{1}{F}=\frac{1}{F_1}+\frac{1}{F_2}$
where the terms have their usual meaning.