Question
Question: Refractive index of diamond with respect to glass is \( 1.6 \) and the absolute refractive index of ...
Refractive index of diamond with respect to glass is 1.6 and the absolute refractive index of glass is 1.5 . Find out the absolute refractive index of diamonds.
(A) 1.06
(B) 0.93
(C) 2.4
(D) 0.75
Solution
Hint : The absolute refractive index is the refractive index when the medium is present in a vacuum that is to say, the ratio of the speed of light in vacuum to the speed of light in the medium. The relative refractive index is the ratio of the absolute refractive index of the substance to the absolute refractive index of the reference substance.
Formula used: In this solution we will be using the following formula;
n12=n2n1 , where n12 means the refractive index of substance 1 relative to substance 2, n1 is the absolute refractive index of substance 1, and n2 is the absolute refractive index of substance 2.
Complete step by step answer
In general, just like light can travel from vacuum or air into a particular substance, it can also travel from that substance into another substance. The bending of light rays as it goes from one medium (that is not vacuum) into another medium (also not vacuum) constitute what we call the relative refractive index.
When light goes from vacuum to a medium that constitutes what is called the absolute refractive index.
In our question, the relative refractive index of diamond relative to glass is known, we are to find the absolute refractive index. The relative index is given as
n12=n2n1 , where n12 means the refractive index of substance 1 relative to substance 2, n1 is the absolute refractive index of substance 1, and n2 is the absolute refractive index of substance 2.
For diamond relative to glass, we can say
ndg=ngnd
Hence,
ndg=1.5nd=1.6
Then by cross-multiplying
nd=1.6×1.5=2.4
Hence, B is the correct option.
Note
For clarity, the relative refractive index of a substance 1, relative to another substance 2 is defined as the ratio of the speed of light in substance 2 to the speed of light in substance 1. i.e.
ndg=vdvg