Question

A boy uses blue colour of light to find the refractive index of a glass. He then repeats the experiment by using red colour of light. Will the refractive index be the same or different in both the cases? Give a reason to support your answer.

Answer 1

Refractive index tells us the change in speed of propagation of light from air or vacuum to another medium because due to refraction light gets deflected from its path when the medium is changed and so the velocity. Here the medium is glass that is light travels from air to glass. To get the solution we will discuss the refractive index and the factors of which it depends.
Formula used:

& \eta =\dfrac{c}{f\lambda } \\\ & v=f\lambda \\\ \end{aligned}$$ **Complete answer:** Refractive index is the quantity which tells us the change in speed of light when it travels from one medium to another and it is given as the ratio of speed of light in vacuum to the phase velocity i.e. velocity of light in another medium (for example, water, glass, etc.). Formula for refractive index is $$\eta =\dfrac{c}{v}$$ Where c is the speed of light in vacuum which is constant and v is the phase velocity. Now as per the question we have to find a relation between wavelength and refractive index. Velocity can be given in terms of wavelength, velocity is given as a product of wavelength and frequency. $$v=f\lambda $$ Now substituting the value of the velocity in the formula for refractive index we get $$\eta =\dfrac{c}{f\lambda }$$ Hence we can say that the refractive index will vary inversely with wavelength. Greater wavelength will have a smaller refractive index. And we know that the wavelength of red light is greater than the blue light, therefore the refractive index of glass for red light will be smaller than the refractive index of blue light. **Note:** Speed of light is constant but it may slow down due to change in media and this changed speed is given as phase velocity. As the refractive index also depends on the medium, in a denser medium light gets bended towards normal, hence the refractive index will be greater. For a rarer medium the case will be opposite.