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# Light: Refractive Index

Aug 19, 2022

## Key Concepts

• Reason behind the bending of light.
• Absolute refractive index
• Angles of incidence, refraction and emergence.

## Introduction:

It is known that a ray of light bends on moving from one medium to another. However, the reason for this bending and a measure of this bending will be discussed in this sections.

### Reason behind refraction of light:

• When light traveling in the air enters a glass slab, it bends. This is because when light moves from one medium to another, it bends.
• When light enters a glass medium from the air, it gets difficult to travel through it, as glass is denser than air. Therefore, the speed of light reduces in the glass.
• The speed of light in the air or vacuum is 3 × 108 m/s, which gets reduced approximately to
2 × 108 m/s in glass.
• The light, therefore, takes a shorter path through the glass slab by bending slightly towards the normal.
• This way, the light gets through the glass slab in the same time as it would have taken in the absence of the glass slab.
• Similarly, when light leaves a glass medium to enter the air, it gets easier to travel through it, as air is rarer than glass. Therefore, the speed of light increases again to its original value,
3 × 108 m/s
• Hence, light bends away from the normal, as it has reached the same velocity again.
• Thus, a ray of light shifts laterally on getting refracted through a glass slab.

### Refractive index:

• Refractive index is a measure of the amount of bending or the change in speed of light when it enters a medium from the air.
• It is usually denoted by the letter n
• The absolute refractive index of a medium is the ratio of the speed of light in vacuum or air and in the medium.

That is, n = c/v

• Where c (= 3 × 108 m/s) is the speed of light in vacuum or air and v is its speed in the medium.
• Refractive index of air is,

nair = c/c = 1, which is the minimum value of all.

• As here the first and the second medium, both are air, the velocity remains c = (= 3 × 108 m/s).
• The refractive index of any other medium is greater than 1, as the velocity v in that medium is always less than c. As a result, n >= 1
• The refractive index of a medium is unitless
• Absolute refractive index of glass is,
• That is, nglass =  c/v = 3 x 108 m/s / 2 x 108 m/s = 1.5

As here the first and the second medium, both are air, the velocity remains c = (= 3 × 108 m/s).

• The absolute refractive index of water can be calculated similarly to yield 1.33.

nwater = 1.33

• Therefore, nglass > nwater
• This means that glass bends a light ray more than water

Angles of incidence, refraction and emergence:

The angle of incidence is not equal to the angle of refraction, as the refracted ray either bend towards or away from the normal, changing its inclination with the normal line. Therefore,

i ≠ ∠r

#### Normal incidence:

However, in normal incidence, the incident ray goes along the normal or parallel to the normal as shown. Here, the light ray passes through the second medium without bending at all.

Therefore, in this case, i = ∠r = 0 degrees.

In all other cases, the above relation does not hold.

The incident ray is always parallel to the emergent ray in case of refraction through a glass slab.

Therefore,i = ∠e.

## Summary:

1. The speed of light in a vacuum or air is 3 x 108m/s.

2. The light bends towards the normal on entering a denser medium in order to cover a shorter path in the same time, as its speed is reduced in that medium.

3. The speed of light increases to become 3 x108 m/s as it comes out of a denser medium back to air. Thus, it bends away from the normal.

4. Aray of light undergoes a lateral shift on passing through a glass slab after refraction.

5. Refractive index is a measure of the amount of bending or the change in speed of light when it enters a medium from air.

6. The absolute refractive index of a medium is the ratio of the speed of light in vacuum or air and in the medium. That is, n= \$where c is the speed of light in air and visits speed in the medium.

7. The refractive index of air or vacuum is 1, which is the minimum value of all.

8. The angle of incidence is not equal to the angle of refraction, except for normal incidence.

9. The angle of incidence is always equal to the angle of emergence.

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