Question

Which colour of white light travels slowest, in glass
a). Blue
b). Violet
c). Red
d). Yellow

Answer 1

Hint: The speed of different colors of white light in different mediums depends on the wavelength of monochromatic light. Greater the wavelength implies faster the monochromatic light travels in the particular medium. Therefore using this information we will first see which of the above given colors of light have the least wavelength and accordingly conclude that it will travel the slowest amongst the alternatives provided.

Formula Used:
$\eta =\dfrac{V}{v}=\dfrac{{{\lambda }_{\text{V}}}}{{{\lambda }_{\text{M}}}}$

Complete step by step answer:
Light basically consists of seven colors. These colors are Violet, Indigo, Blue, Green, Yellow, Orange and Red. The above colors mentioned are in the order of increasing wavelength. The refractive index for Red is smaller than that of refractive index for violet which has the least wavelength amongst the remaining colors. Refractive index($\eta $ ) for any substance is defined as the ratio of speed of light in vacuum(V) to the speed of light in the medium(v). It is also defined as the wavelength of a particular light in vacuum (${{\lambda }_{\text{V}}}$)to its wavelength in the medium(${{\lambda }_{\text{M}}}$ ). Mathematically this can be represented as,
$\eta =\dfrac{V}{v}=\dfrac{{{\lambda }_{\text{V}}}}{{{\lambda }_{\text{M}}}}$
The speed of light in vacuum for either wavelength of light is the same. Since refractive index for Red or any other color is smaller than Violet, we can imply that the speed of light in the medium having any refractive index will be the least for Violet.

Therefore the correct answer for the above question is option b.

Note:
We basically get the refractive index in terms of wavelength of light used, because when the light enters from one medium to another, the frequency of light remains the same. It is only that the wavelength of light changes. In general we can say that any wavelength of light having the least wavelength will travel the slowest in comparison to those whose respective wavelengths is greater than the one with the least.