Question

The speed of light in a certain substance is 88.9 % of its value in water. What is the index of refraction of this substance?

Answer 1

We know that speed of light in air is c_air =3*10⁸m/s

nwater = refreactive index of water = 1.33

Now speed of light in water is c_water =c_air/nwater =  3*10⁸m/s/1.33 = 2.25*10⁸m/s

Now given that  speed of light in  certainsubstance is c_s = 88.9% of c_water

                                                                                     = 0.889*2.25*10⁸m/s = 2*10⁸m/s

Then we know that c_s =c_air/n_substance

                            2*10⁸m/s=  3*10⁸m/s/n_substance

Thus  index of refraction of this substance isn_substance = 1.5