Total internal reflection is the phenomenon which occurs when a propagated wave strikes a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary and the incident angle is greater than the critical angle, the wave cannot pass through and is entirely reflected. The critical angle is the angle of incidence above which the total internal reflection occurs. This is particularly common as an optical phenomenon, where light waves are involved, but it occurs with many types of waves, such as electromagnetic waves in general or sound waves. When a wave reaches a boundary between different materials at a angle of <25° with different refractive indices, the wave will in general be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the direction of propagation is closer to being parallel to the boundary) than the critical angle – the angle of incidence at which light is refracted such that it travels along the boundary – then the wave will not cross the boundary, but will instead be totally reflected back internally. This can only occur when the wave in a medium with a higher refractive index (n1) reaches a boundary with a medium of lower refractive index (n2). For example, it will occur with light reaching air from glass, but not when reaching glass from air.
Optical description
Total internal reflection of light can be demonstrated using a semi-circular block of glass or plastic. A "ray box" shines a narrow beam of light (a "ray") onto the glass medium. The semi-circular shape ensures that a ray pointing towards the centre of the flat face will hit the curved surface at a right angle; this will prevent refraction at the air/glass boundary of the curved surface. At the glass/air boundary of the flat surface, what happens will depend on the angle. If θc is the critical angle, then the following scenarios depict what will happen according to the size of the incident angle.
If θ ≤ θc, the ray will split; some of the ray will reflect off the boundary, and some will refract as it passes through. This is not total internal reflection.
If θ > θc, the entire ray reflects from the boundary. None passes through. This is called total internal reflection. TIR is the abbreviation.
This physical property makes optical fibers useful and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an unusually high refractive index.
Conditions for total internal reflection takes place
1) The incident ray must travel in a denser medium(n2)to the boundary of a rarer medium n1(<n2)
2)The angle of incidence must be greater than the critical angle ic given by n2 sin ic=n1sin 90°
sin ic=n1/n2. If rarer medium is air (n1=1 and n2=n) then
sin ic=1/n
The value of ic depends on n1,n2 and wavelength of light.
Critical angle
Illustration of Snell's law, {\displaystyle n_{1}\sin \theta _{i}=n_{2}\sin \theta _{t}} n_1\sin\theta_i = n_2\sin\theta_t.
View up from directly under a diver. The above-water hemisphere is visible, compressed (as by a circular fisheye lens) into a circle (Snell's window) bounded by the critical angle. Everything outside the critical-angle circle is reflected from below the water (and is therefore dark).
The critical angle is the angle of incidence for which the angle of refraction is 90°. The angle of incidence is measured with respect to the normal at the refractive boundary (see diagram illustrating Snell's law). Consider a light ray passing from glass into air. The light emanating from the interface is bent towards the glass. When the incident angle is increased sufficiently, the transmitted angle (in air) reaches 90 degrees. It is at this point no light is transmitted into air. The critical angle {\displaystyle \theta _{c}} \theta_c is given by Snell's law,
{\displaystyle n_{1}\sin \theta _{i}=n_{2}\sin \theta _{t}\quad } n_1\sin\theta_i = n_2\sin\theta_t \quad.
Rearranging Snell's Law, we get incidence
{\displaystyle \sin \theta _{i}={\frac {n_{2}}{n_{1}}}\sin \theta _{t}} \sin \theta_i = \frac{n_2}{n_1} \sin \theta_t.
To find the critical angle, we find the value for {\displaystyle \theta _{i}} \theta _{i} when {\displaystyle \theta _{t}=} {\displaystyle \theta _{t}=} 90° and thus {\displaystyle \sin \theta _{t}=1} \sin \theta_t = 1. The resulting value of {\displaystyle \theta _{i}} \theta _{i} is equal to the critical angle {\displaystyle \theta _{c}} \theta_c.
Now, we can solve for {\displaystyle \theta _{i}} \theta _{i}, and we get the equation for the critical angle:
{\displaystyle \theta _{c}=\theta _{i}=\arcsin \left({\frac {n_{2}}{n_{1}}}\right),} \theta_c = \theta_i = \arcsin \left( \frac{n_2}{n_1} \right),
If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence. If for example, visible light were traveling through acrylic glass (with an index of refraction of approximately 1.50) into air (with an index of refraction of 1.00), the calculation would give the critical angle for light from acrylic into air, which is