Question

The wavelengths for the light of red and blue colors are roughly $7.8\times 10^{-7} m\ and\ 4.8\times 10^{-7}m$ respectively. Which color has the greater speed in glass?
A. Red light
B. Violet light
C. Yellow light
D. All colors have same speed

Answer 1

Hint: Light is that part of the electromagnetic spectrum which is visible to us. Light consists of seven colors which are collectively known as VIBGYOR. According to Cauchy, different colors have different refractive index for a particular material. This is the reason why if the light is passed through a prism, it splits into various colors.

Complete answer:
According to Cauchy’s equation, the refractive index and the wavelengths are inversely related. Hence if the wavelength of the wave is increased, its refractive will decrease for that wave. Hence speed, which is directly related to the wavelength also increases.
Thus, light with maximum wavelength will have maximum velocity whereas light with minimum wavelength will have minimum velocity in a particular medium.
Now, as we read VIBGYOR- It means Violet, Indigo, Blue, Green, Yellow, Orange and Red, we read it in the order of increasing wavelengths. Hence we see that red light has the maximum wavelength and violet light will have minimum wavelength. Thus red light has the maximum or greater speed than any other color from VIBGYOR.
Thus, option A is correct.

Additional information:
Cauchy gave an equation relating wavelength and refractive index:
$\mu = A\ +\ \dfrac{B}{\lambda^2} + \dfrac{C}{\lambda^4} + . . . .$, where A, B, C,. . . are constants.
This equation is not important for students. This is just shown for reference.

Note: Students might not be confused about the frequency of light waves. Frequency is wholly the property of source of light. Unlike wavelength, it can't be changed by medium or external conditions.
But wavelength can be changed by external conditions and hence wave velocity also gets changed by relation $v=\mu \lambda$.