Question

For which colour of the light is:

1. angle of refraction maximum?
2. focal length maximum?

How does the refractive index of glass vary with colours?
Is dispersion possible in lenses?

Answer 1

Focal length of a lens depends on the refractive index of the material of the lens according to the relation
$\frac{1}{f}=(\mu -1)(\frac{1}{R_1}-\frac{1}{R_2})$.....................(i)
AND refractive index of the material also depends on the wavelength of light passing through through the material of the lens according to the relation $\mu isproportionalto\frac{1}{\lambda }$............................(ii)
from equation (i) and (ii) , we can say that f is proportional to $\lambda$( wavelength )

now $$\begin{gathered} {\lambda }_R(wavelenghtofred)>{\lambda }_V(waveleghtofviolet) \\ \Rightarrow f_R>f_V \end{gathered}$$
HENCE FOCAL LENGTH FOR VIOLET COLOUR LIGHT IS MINIMUM.
Refractive index $\mu =\frac{\sin i}{\sin r}$.......................(iii)
from equation (ii) refractive index of a medium will be minimum for red colour.
from equations (ii) and (iii) we can drive the conclusion that angle of reflection will be maximum for red colour wavelength.