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5.3 Total Internal Reflection

What is meant by ‘ Total Internal Reflection ‘

The total reflection of a beam of light at the interface of one medium and another medium of lower refractive index

(optically less dense) , when the angle of incidence to the second medium exceeds a specific critical angle.

Ray diagram to show how the Total Internal Reflection happen ?

clip_image002(1)  Angle of incidence ,i1 is small.Produces a strong refracted ray and a weak reflected ray.

(2) Angle of incidence is increased as i2.Produces a  refracted ray and a reflected ray whose intensity has increased compared to the situation in (1)

(3)     Angle of incidence is increased to the critical angle, c.The refracted ray travels along the water-air boundary.

(4)     Angle of incidence , i3  > c.No refraction occurs.All the light is reflected within the water .Total internal reflection occurs.

The conditions for the occurrence of total internal reflection.


(1)     The light ray must be travel from an optically denser medium to less dense medium.   

(2)     The angle of incidence must be greater than the critical angle.


The Critical Angle, c

The angle of incidence in an optically more dense medium which results in angle of refraction of 90o   in  an optically less dense.

Determine the relationship between Refractive index (n) and Critical angle (c)


  n = sin i

                      sin r

Example 1

The diagram shows a light ray entering in a glass prism.

[ Refractive index of glass = 1.51 ]


                (a)   Determine the critical angle of the glass.

(b)     Draw the ray light after it passes through a point P until the direction of the ray of light unchanged.




Example 2

Figure shows a light ray AO travelling from medium X  to the air.

[The refractive index of medium X = 2.0 ]



Draw the ray light after it passes through the point  P  when

(a) q = 25o     (b)q = 30o   (c) q = 35o 



Experiment to determine the critical angle of  glass.


A semi-circular glass block  is placed on a sheet of white paper.

The outline of the glass block is traced onto the paper as ABC.

The glass block is put aside.

A normal ON is drawn.

The glass block is placed again on its outline.

A ray of light  from the ray box is directed to glass block.

The angle of incidence is increased until the refracted ray travels along the length of the air- glass boundary  ( refraction angle is 90o ).

By using a protractor  the angle of incidence is measured = c

The critical angle of the glass block = c

Natural phenomena and Use of Total Internal Reflection.




In the time when the weather is hot , the incidence ray from the sun passes through a dense air layer to a less dense air layer.

Finally , the ray of passes through the air layer close to the road surface at an angle of incidence greater than the critical angle.

Total internal reflection occurs at this layer.

The observer sees the image of the sky on the surface of the road as a pool of water.


Prism periscope


The periscope is built using two right –angled prisms made of glass .

The critical angle of the prism is 42o .

The angle of incidence is 45o is greater than the critical angle.

Total internal reflection occurs.  

The characteristics of the images are

(i)  Virtual   

(ii) Upright  

(iii) Same size as the object.

Advantages  of the prism periscope compared to mirror periscope,

(i)            The image is brighter

(ii)           No multiple images is formed (very clear)



A ray light experiences two total internal reflections at each prism. The two prisms is to invert the image (upside down and right-to-left.) But the lenses in the binoculars also invert the image and so the the prisms put it back the right way again.

So the final image in binoculars is upright ,not laterally inverted and magnified.


 Fibre  optics



The external wall of a fibre optic is less dense than the internal wall.

When light rays travel from a denser internal wall to ales dense external walls at an angle that exceeds the critical angle , total internal reflection occurs.

The advantages of the fibre optics:

(i)            Cheap

(ii)           easily handled

(iii)          More information can be transmitted


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