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Question

How is the refractive index of a medium related to the speed of light? Obtain an expression for the refractive index of a medium with respect to another in terms of speed of light in these two media?


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Solution

Step 1: Refractive index:

  1. Refractive index of a medium is defined as the ratio of the velocity of light in air and the velocity of light in that medium.
  2. Refractive index, μ=cv, c is the velocity of light in air and v is the velocity of light in the medium.

Step 2: Finding the relative refractive index:

Let v1 and v2 are the velocities of light of mediums 1 and 2 respectively. And μ1 and μ2 are their refractive indices.

Now, the refractive index of the first medium, μ1=cv1 and the refractive index of the second medium, μ2=cv2, where c is the velocity of light in air.

The refractive of the second medium with respect to the first is 1μ2,

1μ2=μ2μ1=cv2cv1=v1v2.

1μ2=v1v2.

Therefore, the refractive index of the second medium with respect to the first is v1v2.


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