# Total Internal Reflection (T.I.R)

# Total Internal Reflection (T.I.R)

Critical Angle (i_c):

“The angle of incidence in the dense medium for which the angle of refraction in the rarer medium is 90^° is called as critical angle.”

T.I.R:-

“When the angle of incidence of a light ray travelling from denser medium to rarer medium, is greater than the critical angle, the ray gets totally reflected book into the denser medium.”

This phenomena is called as T.I.R

# Conditions for T.I.R:

(i) Light ray should travel from denser medium to rarer medium.

(ii) The angle of incidence should be greater than the critical angle.

# Relation between refractive index (N) and critical

By Snell’s law at pt. P                    

^bµ_a = sin i/sin r

∴ ^bµ_a = sin i_c/sin 90^° = sin i_c

Or (1/^aµ_b) = sin i_c

Or (^aµ_b) = (1/sin i_c)  or (c/υ) = (1/sin i_c)

µ → increases,       i_c→ decreases

υ → increases,       i_c→ increases

λ → increases,       i_c→ increases

Note:- sin i_c µ ∝ (1/sin i_c) and µ ∝ (1/ λ²)      ∴ sin i_c ∝ λ²

# Applications of T.I.R :→

(i) Mirage:-

It is an optical illusion observed in deserts on a hot summer day.

On a hot summer day, the temperature of the air near the surface of earth becomes higher & that of the upper layers decreases gradually.

Since density ∝ (1/temperature)

∴ density increases gradually above the surface of earth.        

A ray of light coming from the object travels from denser to rarer medium and bends more and more away from the normal. At a particular stage, when the angle of incidence becomes greater than the critical angel, total internal reflection (T.I.R) takes place.

To an observer, the ray appears to be coming from I and hence inverted image of the object is seem and it seems as if water is there. 

(2) Optical Fibres:

Optical Fibres consist of very fine quality glass or quartz of refractive index = 1.7. The fibres are coated with a thin layer of material of lower refraction index = 1.5

When light is incident on one end of the fibre, it undergoes total internal reflections inside the fibre and finally comes out.           

Uses:

(i) A bundle of optical fibres (light pipe) is used in medical and optical examination of even the in a –cc essible parts of human body.

(ii) These are used for transmission and reception of electrical signals by first converting them into light signals.

(iii) These are used in telephone & other transmitting cables.

(3) Brilliance of diamond:

Refractive index of diamond is 2.42 so the critical angle for diamond air interface is 24.4^°. The diamond is cut in such a way that light entering the diamond from any face undergoes total internal reflections at various faces and remains within the diamond. Hence diamond shines very brilliantly.

(4) Totally reflecting prisms:

These are the right angled isosceles prisms which turn the light through 90^° or 180^°.

The critical angle (i_c) for glass-air interface is 42^°. In totally reflecting prisms, angle of incidence is made 45^° (> i_c) ∴ light suffers T.I.R.