Question

What is the formula for refraction through spherical Lens when the refractive index of the medium on two sides of lens are different ?

Answer 1

Refraction at Spherical Surface

Distance of object and image from spherical pole is $uandv$

Redfractive index of rarer medium and denser medium is ${\mu }_{1}and{\mu }_2$

We get,

$\tan \alpha =\frac{MN}{OM},\tan \beta =\frac{MN}{MI}and\tan \gamma =\frac{MN}{MC}$

Now, for Δ NOC

$i=\angle NOM+\angle NCM$

$i=\frac{MN}{OM}+\frac{MN}{MC}$ …….1

Similarly,

$r=\frac{MN}{MC}\text{+}\frac{MN}{MI}$ …….2

Now by using Snell’s law we get

${\mu }_{1}sini={\mu }_{2}si{n}_{}r$

Substituting i and r from Eq. (1) and (2), we get

$\frac{{\mu }_1}{OM}+\frac{{\mu }_2}{MI}=\frac{{\mu }_2-{\mu }_1}{MC}$

As $OM=-u,MI=+v,MC=+R$

Hence, the equation becomes, $\frac{{\mu }_2}{v}\text{-}\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$