Question

Refractive index of water with respect to air is 1.33 and that of diamond is 2.42. 

(i) In which medium does the light move faster, water or diamond? 

(ii) What is the refractive index of diamond with respect to water?

Answer 1

Refractive index = \(\frac{speed\,of\,light\,in\,vacuum}{speed\,of\,light\,in\,medium}\)

Since the refractive index of diamond is more, hence the speed of light is lesser in diamond. 

Let speed of light in water vev_w and in diamond bev_d. 

Refractive index of diamond w.r.t water is say n = \(\frac{speed\,of\,light\,in\,water}{speed\,of\,light\,in\,diamond}\)

\(n=\frac{V_w}{V_d}\)

Dividing both numerator and denominator by speed of light [c] we get 

n = (\(\frac{V_w}{c}\)) ÷ (\(\frac{V_d}{c}\)) = Inverse Ratio of refractive index of water and diamond. 

n=\(\frac{2.42}{1.33}\) = 1.82 (approx)