Question

Explain refraction using ray diagrams. Give an example for the refraction of light.

Answer 1

Light rays travel in different mediums at different speeds. In vacuum, for example, light travels at the speed of 3×108 m/s. This is the highest speed possible in physics.

One of the most important parameters that measures optical properties of a medium is the index of refraction. It is defined as the ratio of the speed of light in vacuum (3×108m/s) and the speed of light v in the medium in question. 
The refractive index measure the optical density of a given material. A material with higher refractive is more optically dense than a material with lower refractive index.

n =  

c

v

Example 1 

What is the index of refraction in a medium where the speed of light is 1.5×108 m/s?

Solution

n =  

c

v

=  

3×108 m/s

1.5×108 m/s

= 2

Example 2 
What is the speed of light in water whose refractive index is 1.33?

Solution

1.33 =  

3×108 m/s

v

v =  

3×108 m/s

1.33

≈ 2.26×108 m/s

A homogeneous medium has a constant index of refraction throughout the medium and light travels along straight paths in it. Refraction occurs at the interface or boundary of two media with different refractive indices. It is the bending of light rays when transmitted into the second medium.(see diagram below)



Snell's Laws of refraction 

1) The incident ray, the refracted ray and the normal to the interface at the point of incidence are all included in the same plane called the plane of incidence. 

2) n1 sin (i) = n2 sin (t) 

where n1 is the refractive index of medium (1), n2 is the refractive index of medium (2), i is the angle of incidence and t is the angle of refraction as shown in the diagram above.

Refraction explains physical phenomena such the appearance of a pen bent inside a glass of water and the separation of white light into different colors such as the rainbow as shown below.





Example 3 
A ray of light is incident through glass, with refractive index 1.52, on an interface separating glass and water with refractive index 1.32. What is the angle of refraction if the angle of incidence of the ray in glass is 25 °?



Solution 
Use Snell's law to write: 1.52 sin 25° = 1.32 sin t 
t = arcsin((1.52/1.32) sin 25) ≈ 29.1 °