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# Light: Multiple Refractions

Aug 18, 2022

## Introduction:

A light ray bends when it travels from one medium to another, and it bends either towards or away from the imaginary normal line while doing so. When the light ray traveling in the air enters a glass slab or water, it bends towards the normal. And, when it is traveling in the glass or water and enters the air, it bends away from the normal. In this section, we will be throwing some light on the kind of refraction that a light ray undergoes when it encounters more than two mediums.

### Multiple refractions:

A ray of light undergoes multiple refractions when it encounters more than one transparent mediums one after the other. At every step, it either bends towards or away from the normal depending upon the refractive indices of the current and the upcoming medium.

For example,

When a light ray falls on the water in a glass tumbler, it undergoes many refractions so that it comes out of it from the bottom. The light refracts,

1. From air to water
1. Then from water to the glass base of the tumbler
1. Finally, from the glass base back to the air from the bottom of the tumbler

Note: Bending of light

Suppose the refractive indices of two mediums be n1 and n2

1. If n1 < n2, then the refracted ray bends towards the normal.
1. If n2 > n1, then the refracted ray bends away from the normal.

Explanation:

Refractive index of air (1) is smaller than that of water (1.33), i.e., at the air-water interface,

nair < nwater

Thus, the refracted ray bends towards the normal.

Refractive index of water (1.33) is smaller than that of glass (1.5), i.e., at the water-glass interface,

nwater < nglass

Thus, the refracted ray bends towards the normal again.

Refractive index of water (1.33) is smaller than that of glass (1.5), i.e., at the glass-air interface,

nair < nglass

Thus, the refracted ray bends away from the normal.

When the light ray enters the tumbler from the bottom, it gets refracted in the following way:

At the air-glass interface,

nair < nglass

Thus, the refracted ray bends towards the normal.

At the glass-water interface,

nglass > nwater

Thus, the refracted ray bends away from the normal.

At the water-air interface,

nwater > nair

Thus, the refracted ray bends away from the normal.

### Normal incidence:

A light ray incident normally on the glass surface goes straight into all the mediums along the normal line and emerges without any deviation from its path.

Note:

In all the above refractions, the emergent ray is parallel to the incident ray, even if a light ray suffers multiple refractions before emerging into the first medium (air).

### Question:

Kerosene and water have refractive indices of 1.44 and 1.33, respectively. Kerosene floats on the top of water, as shown. A light ray from the air enters the kerosene, then the water and then back to the air. Identify the way in which the light ray would bend in every step? Is the emergent ray parallel to the incident ray?

Given that,

The refractive index of kerosene, nk = 1.44.

The refractive index of water, nw = 1.33.

And the refractive index of air, na = 1.

nk > na

Thus, the refracted ray bends towards the normal.

At the kerosene-water interface,

nk > nw

Thus, the refracted ray bends away from the normal.

At the water-air interface,

nw > na

Thus, the refracted ray bends away from the normal.

Yes, the emergent ray E is parallel to the incident ray I.

## Summary:

• A ray of light undergoes multiple refractions when it encounters more than one transparent mediums one after the other.
• At every step, it either bends towards or away from the normal depending upon the refractive indices of the current and the upcoming medium.
• However, during normal incidence, the ray of light does not bend at all. It passes straight through all the mediums.
• Even though a ray of light undergoes multiple refractions, it emerges out parallel to the incident ray into the first medium.

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