Total Internal Reflection


 
 
Concept Explanation
 

Total Internal Reflection

When a ray of light travels from denser(higher refractive index) to the rarer (low refractive index) medium, it bends away from the normal . This means that angle of refraction angle r is greater than angle of incidenceangle i. With increase in the angle of incidence, the angle of refraction also increases.The figure below shows the incident ray in red colour, the refracted ray with blue colour and the green colour ray shows the part of ray which is reflected.

At a particular value of   angle i called as critical angle the angle of refraction becomes 90^{circ}.At this angle refracted ray then comes out parallel to the surface seprating the two media The figure below shows the incident ray in red colour, the refracted ray with blue colour and the green colour ray shows the part of ray which is reflected. We see that the blue ray grazes the surface seprating the two media.

The relation between the critical angle and the refractive index is

Refractive; index; of; the; denser; medium ;eta= frac{1}{sin;c}

As we increase the angle above the critical angle it results in reflecting back of the ray into the same medium. This reflection obeys the law of reflection therefore angle of reflection angle r^xof ray  is equal to the angle of incidenceangle i   above the critical angle. The figure below shows the incident ray in red colour, As the angle of incidence is more than the critical angle there is no refracted ray hence there is no blue coloured ray and the green colour ray shows the reflected ray, which follows the laws of reflection..

Thus the total internal reflection of light takes place when a ray of light travels in a denser medium and is incident on the boundary with rarer medium at an angle greater that the critical angle. It is known as total reflection because when a ray falls obliquely on the interface of the two transparent medium, a part of it is reflected and a part of it is refracted. When the angle of incidence is greater than critical angle, the whole  of the light ray is reflected. Hence it is called total internal reflection.

For angle i= i_c and angle r= 90^0, from Snell's law

frac{sin;i}{sin;r}= frac{eta_2}{eta_1}

Substituting the values of i and r, we get

frac{sin;i_c}{sin;90^0}= frac{eta_2}{eta_1}

Rightarrow ;;frac{sin;i_c}{1}= frac{eta_2}{eta_1}

Rightarrow ;;sin;i_c= frac{eta_2}{eta_1}=; _1eta_2

 

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Sample Questions
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Question : 1

Which of the following are correct  ?

(a)  When a ray of light travels from rarer to the denser medium, it bends away from the normal .With increase in the angle of incidence, the angle of refraction also increases.

(b) When the angle of incidence is greater than critical angle, the whole  of the light ray is reflected. Hence it is called total internal reflection .

(c) The critical angle is different for different pairs of media.

Right Option : B
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Explanation
Question : 2

Which of the following are correct ?

(a)  When a ray of light travels from high refractive index to the low refractive index medium, it bends away from the normal. 

(b)  Total internal reflection obeys the law of reflection therefore angle of reflection of ray  is equal to the angle of incidence   above the critical angle.

(c) The higher the refractive index eta_1  of the denser medium, the smaller is the critical angle for the pair.

Right Option : D
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Explanation
Question : 3

Rainbow formation involves the process of

Right Option : B
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Explanation
 
 
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