# Question #b0756

Mar 22, 2017

By wave theory the refractive index $\mu$ of a medium with respect to air for a particular color of light is related with the velocity of that light in air (${v}_{\text{air}}$) and velocity of that light in that medium (${v}_{\text{med}}$) as follows

$\mu = {v}_{\text{air"/v_"med}}$

Again by Snell's law

$\mu = \sin \frac{i}{\sin} r$,where i and are angle of incidence and angle of refraction respectively.

So

$\mu = {v}_{\text{air"/v_"med}} = \sin \frac{i}{\sin} r$

This relation suggests that the angle of incidence remaining same angle of refraction decreases with increase of refractive index causing greater deviation or greater bending of ray due to refraction.

This decrease in angle of refraction also indicates that the ${v}_{\text{med}}$ also decreases with the increase in refractive index of the medium or increase in bending of ray due refraction.

Conclusion

When colour X and colour Y are sent through a prism.

If color X bends more than color Y, then the refractive index of the prism for color X is greater than R.I with respect to color Y . And so velocity of X is less than that of Y through the prism. This means Y will travel more rapidly in the prism.