Refraction of lightCopy

Learning Objectives

• Describe an experimental demonstration of the refraction of light
• Use the terminology for the angle of incidence i and angle of refraction r and describe the passage of light through parallel-sided transparent material
• Give the meaning of critical angle
• Describe internal and total internal reflection
• Recall and use the definition of refractive index n in terms of speed
• Recall and use the equation n = sin i / sin r 
• Recall and use n = 1 / sin c
• Describe and explain the action of optical fibres particularly in medicine and communications technology

Contents to learn

Refraction of light

When light ray enters from one medium to the other medium, it changes its direction in the second medium depending upon the angle of incidence because of the change in speed.

When the light ray enters from denser medium to the rare medium, it bends away from the normal. Its speed and wavelength increases but frequency remains same. Direction of refracted wave depends upon the direction of incident wave.

When light ray enters from rare medium to the denser medium, it bends towards the normal. Its speed and wavelength decreases but frequency remains same.

Direction of refracted ray of light depends upon the direction of incident ray of light.

Law of refraction:

When light ray refracts, it obeys the law of refraction which is as under.

1-Sine of Angle of incidence is directly proportional to the Sine of Angle of refraction.

2- Incident ray, refracted ray and normal all they lie in the same plane.

Important to note:

1- Angle of incidence is the angle between incident ray and the normal to the boundary of the first medium

2- Angle of refraction is the angle between the refracted ray and the normal to the boundary of the second medium, in which light ray enters

3- In refraction phenomenon, direction, wavelength and the speed change but frequency remains same.

4- In refraction phenomenon, if angle of incidence is zero (means ray is coming along the normal) then angle of refraction will also be zero and the wave goes straight in the second medium without bending, but speed and wavelength changes depending upon the nature of the second medium in which it is entering.

5- In this syllabus we study three media, glass, water and air. Glass is most dense medium, then water and water which is denser than air. In water we study two regions shallow and deeper, deeper is the rare medium as compare to the shallow region.

6- Ratio of Sin i to the Sin r is always constant for a particular medium, which is called the refractive index.

Critical angle
It is the angle of incidence in the denser medium for which angle of refraction in the rare medium is 90o.

Critical angle and the refractive index are related by the relation

Refractive index (n) = 1 / Sin C

OR

Sin C = 1 / Refractive index (n)

Total internal reflection

When ray of light enters from denser medium to the rarer medium they move away from the normal.

As the angle of incidence increases, an angle is reached at which the light rays will have to leave with an angle of refraction greater than 90o. These rays cannot refract, so they are entirely reflected back inside the medium. This process is known as total internal reflection.

In other words we can say that if angle of incidence is greater than the critical angle, total internal reflection takes place.

Refractive index

The refractive index of a material indicates how strongly the material changes the direction of the light. It is calculated using the formula

Refractive index = Sin i / Sin r ————- (Use this formula, when ray of light enters from rare to denser medium)

Refractive index = Sin r / Sin i ————- (Use this formula, when ray of light enters from denser to rare medium)

where

i = angle of incidence

r = angle of refraction

The refractive index can also be determined by using the following relation

Refractive index = 1 / Sin C

where C is the critical angle.

We can also use the following equation to determine the refractive index

Refractive index = c / v

where

c = speed of light in vacuum

v = Speed of light in the material

It is important for you to understand the below question.

Q: The refractive index for light passing from glass to air is 0.67. Calculate the angle of refraction of the ray that is refracted at Q into air. The angle of incidence in the glass material is 30o.

Solution:

According to Snells’s law

ngSin θg = na Sin θa ………………………………. 1 (In this equation g is used for glass and a is used for air)

As in the question, direct value of the refractive index of the material is not given, but the value of refractive index for light passing from glass to air is given, 0.67 so we have the value of nga = refrective index of air / refrective index of glass = na / ng = 0.67

Rearranging the equation 1

Sin θg = (na / ng ) Sin θa

Sin 30 = ( 0.67 ) Sin r

r = Sin-1 (Sin 30 / 0.67)

r = 48.3o Which is the angle of refraction.

In the above diagram, ray of light is not bending at point P, because it is entring the glass along the normal to the boundry, angle of incidence is zero so angle of refraction is also zero.

Fiber-optics
Total internal reflection is used in fiber optic cables. A fiber optic cable is made of a bundle of very thin glass fibers. The light continues along the fiber by being constantly internally reflected.

Telephone and T.V. communications systems are increasingly relying on fibre optics istead of the more traditional copper cables. fibre optic cables do not use electricity and the signals are carried by infrared rays. The signals are very clear as they do not suffer from electrical interference. Other advantages are that they are cheaper than the copper cables and can carry thousands of different signals down the same fibre at the same time.

Bundles of several thousands opticle fibres are use in medical endoscope for internal examination of the body. The bundle will carry an image from one end of the bundle to the other, each fibre carrying one tiny part (one pixel) of the image.