Question

Why does red light travels faster than violet in a transparent medium?

Answer 1

Hint: Recall the wavelength of red light and violet light. Using the relation between velocity, frequency and wavelength, express the velocity of red light in terms of velocity of violet light. Assume the frequency of the visible spectrum be the same for both the lights.

Complete answer:
As we know the speed of light depends on the wavelength of an electromagnetic wave. The red light and violet light falls in the visible spectrum of the electromagnetic wave. We know that the wavelength of red light is 680 nm while the wavelength of violet light is 410 nm. We have the expression for the speed of a transverse electromagnetic wave,
\[v = f\lambda \]
Here, v is the velocity, f is the frequency and \[\lambda \] is the wavelength.

From the above equation, we can write, \[v \propto \lambda \]. Therefore, we can express the equation for speed of red light and speed of violet light as,
\[\dfrac{{{v_{red}}}}{{{v_{violet}}}} = \dfrac{{{\lambda _{red}}}}{{{\lambda _{violet}}}}\]
Substituting \[{\lambda _{red}} = 680\,{\text{nm}}\] and \[{\lambda _{violet}} = 410\,{\text{nm}}\] in the above equation, we get,
\[\dfrac{{{v_{red}}}}{{{v_{violet}}}} = \dfrac{{680}}{{410}}\]
\[ \therefore {v_{red}} = 1.65{v_{violet}}\]

Thus, the speed of the red light is 1.65 times greater than the speed of violet light assuming the frequency of both lights are the same.

Note:When the light travels from one medium to another medium, only the wavelength and velocity of the light changes. The frequency of the light remains the same in this case. The frequency of the electromagnetic wave depends on the source that produces the electromagnetic wave. You don’t need to do the calculations to show the red light travels faster. Only the relation \[v = f\lambda \] would be sufficient.