Name: Primary Colours of Light
Uploaded: 2019-07-19
Duration: 5 min 33 s
Description: Did you know that certain colours are more important than the others? Also, certain colours can be derived using the others! This video explains why.

Question

If the refractive index of second medium with respect to first medium is

{}_{2}n_{1}

and that of third medium with respect to second medium is

{}_{3}n_{2}

, what and how much is

{}_{3}n_{1}

?

Accepted Answer

Given that,

The relative refractive index of the second medium with respect to the first medium is ${}_{2}n_{1} = \frac{v_{1}}{v_{2}}$ where $v_{1}$ is the speed of light in the first medium and $v_{2}$ is the speed of light in the second medium.

Similarly, the relative refractive index of the third medium with respect to the second medium is ${}_{3}n_{2} = \frac{v_{2}}{v_{3}}$ where $v_{2}$ is the speed of light in the second medium and $v_{3}$ is the speed of light in the third medium.

Then, ${}_{3}n_{1}$ is the relative refractive index of the third medium with respect to the first medium and is ${}_{3}n_{1} = \frac{{}_{3}n_{2}}{{}_{1}n_{2}} = \frac{{}_{3}n_{2}}{\frac{1}{{}_{2}n_{1}}} = \frac{\frac{v_{2}}{v_{3}}}{\frac{1}{\frac{v_{1}}{v_{2}}}} = \frac{v_{2}}{v_{3}} \times \frac{v_{1}}{v_{2}} = \frac{v_{1}}{v_{3}}$ .

Thus, ${}_{3}n_{1} = \frac{v_{1}}{v_{3}}$ .

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