Question

if the refractive index of violet light is replaced by red light how the refractive index and speed of light differs.​

Answer 1

Explanation:

You have it backward, faster speed of light in a material corresponds to less refraction, not more. In the limit that the speed of light in a material was the same as the speed of light in vacuum, there would be no refraction at all.

It can be shown that in a material the index of refraction is the speed of light in vacuum, c divided by the speed of light in the material cm.

n=ccm

So, slower speed in a material corresponds to a larger index of refraction ,and higher speed to a lower index of refraction. The index of refraction is always greater than or equal to 1, because c, the speed of light in vacuum, is always greater than the speed in a material.

So, as you have stated, red light has a lower index of refraction than blue light since it also has a shorter wavelength, so lower index of refraction corresponds to higher speed in a material.Now Snell's Law is stated

n1n2=sinθ2sinθ1

where the geometry is as shown:

enter image description here

So if n1=1.0 and θ1=20 degrees we have

n2=1.51 for red light and θ2=13.09 degrees,

n2=1.53 for blue light, and θ2=12.91 degrees.

• As you can see from the diagram, a smaller value of θ2 corresponds to a larger amount of refraction because it is a larger change in angle and thus a larger change in direction of the incident light.