Refractive Index

Concept Explanation

Refractive Index

Light travels at a speed of $3times10^8$ in vacuum. Light travels at different speeds in different materials because as the light enters any material the atoms of the material absorb, scatter and remit light. Therefore, when it travels from one medium to another, the speed either increases or decreases. The amount by which its speed changes determines the amount by which it will change its direction.

The speed of light in vaccum is $3times10^8$ . The speed of light in a transparent medium such as glass, water or clear plastic is less than this. To calculate the amount by which the ray will deviates from its path we use a physical quantity known as refractive index. It is the ratio of the speed of light in vacuum to the speed light in that medium. As the refractive index is a ratio of two same quantities that is speed it does not have any units.

$Refractive ;Index; eta =frac{Speed; of; light ;in ;Vaccum}{Speed ;of; light; in; that; medium}= frac{c}{v}$

where c = the speed of light in vacuum and v = the speed of light in the medium.

In all material media the speed of light is less than c. Hence, the refractive index of a material medium is greater than 1. The speed of light in air at atmospheric pressure is very close to that in vacuum, and we generally take the refractive index of air as 1.

The refractive index of water is about 1.33, and that of ordinary glass and diamond are about 1.50 and 2.42 respectively.

Larger the refractive index of a medium, greater is the bending of light when it enters the medium from air obliquely. Thus light bends more when it enters a diamond than when it enters an imitation jewel made of glass.

Illustration:: A ray of light enters a diamond from air. If the refractive index of diamond is 2.42, by what per cent does the speed of light reduce on entering the diamond?

Solution: $eta :=:frac{c}{v}$

$v;=;frac{c}{eta }:=;frac{c}{2.42}:=;0.41c$

The speed of light in diamond is therefore 41% of its speed in air. In other words, in diamond, the speed reduces by 59%.

Absolute Refractive Index:

When the refractive index is considered with respect to the vacuum, it is called absolute refractive index.

Relative Refractive Index:

When the light travels from one medium to another medium, the extent of bending of light depends on the refractive index of medium 1 with respect to the refractive index of medium 2. When the light is going from medium 1 to medium 2, the ratio of refractive index of medium 2 to the refractive index of medium 1, is known as relative refractive index.

$Refractive;index ;of; medium ;2 ;w.r.t.; medium ;1 ;(_1 eta _2)=frac{Refractive; Index;of;mediun;2 ;( eta_2) }{Refractive;index;of;medium ;1;( eta_1)}$

$_1 eta _2=frac{ eta_2}{eta_1}=frac{frac{c}{v_2}}{frac{c}{v_1}}= frac{c}{v_2}timesfrac{v_1}{c}= frac{v_1}{v_2}$

So we can say that refractive index of medium 2 w.r.t. the refractive index of medium 1 is ratio of speed of light in medium 1 to the speed of light in medium 2.

Illustration:: Find the refractive index of glass w. r. t. water. The refractive index of glass and water w. r. t. air are 3/2 and 4/3 respectively.

Solution: We know that

$_1 eta _2=frac{ eta_2}{eta_1}$

Here glass is the second medium

$eta_2 =eta_{glass} :=:frac{3}{2}$

And water is the first medium

$eta_1 =eta_{water} :=:frac{4}{3}$

$_{water} eta _{glass}=frac{ eta_{glass}}{eta_{water}}$

$_{water} eta _{glass}=frac{ frac{3}{2}}{frac{4}{3}}= frac{3}{2}times frac{3}{4}= frac{9}{8}$

Illustration: If $_1eta_2$ is the refractive index of medium 2 with respect to medium1, $_2eta_3$ is the refractive index of medium 3 with respect to medium2, and $_3eta_1$ is the refractive index of medium 1 with respect to medium3, then prove that $_1eta_2 times _2eta_3 times_3eta_1= 1$

Solution: We know that refractive index of medium 2 with respect to medium 1

$_1 eta _2=frac{ eta_2}{eta_1}$ ..........[ I ]

And refractive index of medium 3 with respect to medium 2

$_2 eta _3=frac{ eta_3}{eta_2}$ ..........[ II ]

And refractive index of medium 1 with respect to medium 3

$_3 eta _1=frac{ eta_1}{eta_3}$ ..........[ III ]

Using I, II and III, we get

$_1eta_2 times _2eta_3 times_3eta_1= frac{eta_2}{eta_1} timesfrac{eta_3}{eta_2}timesfrac{eta_1}{eta_3}=1$

Hence Proved.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

The refractive index of crown glass is 1.52 and the refractive index of sapphire is 1.77. find the refractive index of crown glass with respect to sapphire
A. 0.86	B. 1.16	C. 0.5	D. 1.25
Right Option : A
View Explanation

Question : 2

If the refractive index of benzene is 1.50, then speed of light in benzene is
A. 3/2 times that in vacuum	B. equal to the speed of light in vacuum	C. 2/3 times that in vacuum	D. 4/3 time that in vacuum
Right Option : C
View Explanation

Question : 3

Which of the following is a unit of refractive Index?
A. m/s	B. degrees	C. Watt	D. Dimensionless
Right Option : D
View Explanation

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Refractive Index

Refractive Index

Absolute Refractive Index:

Relative Refractive Index:

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