Question

SOLVE THIS.. ITS URGENT..​​

Answer 1

Solution:

This formula can be proved only when the prism is kept in air

According to snell's law,

$\implies\mathtt{n_{air} \times sin i = n_{prism} \times sin r }$

As refractive index of air is 1 ,

$\implies\mathtt{1 \times sin i = n_{prism} \times sin r }$

$\implies\mathtt{n_{prism}= \dfrac{sini}{sinr}}....(1)$

Angle of minimum deviation is given by the formula ,

$\implies\mathtt{\delta _{min}= (i+e)-A}$

In case of air , i = e

$\implies\mathtt{\delta_{min} = (i+i)-A}$

$\implies\mathtt{\delta_{min} = 2i -A}$

$\implies\mathtt{i = \dfrac{ \delta_{min} + A}{2} }$

Angle of prism is given by the formula ,

$\implies\mathtt{A= r_1 +r_2}$

In case of air , r 1 = r 2 = r

$\implies\mathtt{A= 2r }$

$\implies\mathtt{r= \dfrac{ A}{2} }$

Substituting the values of i and r in the equation 1 we get,

$\implies\boxed{\mathtt{n_{prism}= \dfrac{sin(\dfrac{ \delta_{min} + A}{2})}{sin(\dfrac{ A}{2})}}}$

Hence proved