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 incidence $angle i$ . 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 $angle r^x$ of ray is equal to the angle of incidence $angle i$ 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

For which of the following cases will the total internal reflection of light be possible?
A. Angle of incidence is less than the critical angle.	B. Angle of incidence is equal to the critical angle.	C. Angle of incidence is greater than the critical angle.	D. Angle of incidence is equal to the angle of refraction.
Right Option : C
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Question : 2

In which of the pairs of media is reflection possible?
A. Air to water		B. Glass to water
C. Both (A) and (B)		D. None of these
Right Option : B
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Question : 3

Total internal reflection takes place when a ray of light travels from ___________________________
A. Denser to the rarer medium		B. Rarer to the denser medium
C. Both A and B		D. None of these .
Right Option : A
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