Question

the refractive index of medium a with respect to medium b is 2/3 and the refractive index of medium b with respect to c is 4/3 . find the refractive index of c with a​

Answer 1

Hey

here is your answer

Answer 2

Refractive index of medium c with respect to medium a is 9/8.

• Refractive index of a medium is defined as the ratio of velocity of speed in air or vacuum to velocity of light in that medium.
• It is dimensionless quantity.
• It is given by

            $n = \frac{velocity of light in air or vacuum}{velocity of light in medium}$

• If light travels from medium 1 to medium 2 then,

            $n_{12} = \frac{velocity of light in medium 2}{velocity of light in medium 1}$

PROBLEM:

• Given,
• Refractive index of medium a with respect to medium b = 2/3

                                       $n_{ab} = \frac{v_{b} }{v_{a} } = \frac{2}{3}$

• Refractive index of medium b with respect to medium c = 4/3

                                        $n_{bc} = \frac{v_{c} }{v_{b} } = \frac{4}{3}$

• Refractive index of medium c with respect to medium a,

                                       $n_{ca} = \frac{v_{a} }{v_{c} } = \frac{v_{a} }{v_{b} }\frac{v_{b} }{v_{c} }\\ = (\frac{3}{2})( \frac{3}{4} )\\ = \frac{9}{8}$