Embibe Experts Solutions for Exercise 1: ICSE-2018

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.

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.

Calculate the focal length of a convex lens whose radii of curvature of two surfaces is $10 \mathrm{cm}$ and $15 \mathrm{cm}$ respectively and its refractive index is $1.5$.

Where will you keep an object in front of a convex lens in order to get a virtual and magnified image?

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.

Derive an expression for refraction at a single(convex) spherical surface, i.e. a relation between $u, v, R, n_1$(rarer medium) and $n_2$(denser medium), where the terms have their usual meaning.$$