Total reflection

Total Internal Reflection

While swimming under water and opening the eyes, one can experience sometimes a mirror like reflection on the surface. This optical phenomenon is called total internal reflection or total reflection. It usually appears when waves of a light source enter from a medium with a higher refractive index (n1) into another one with a lower refractive index (n2). Another condition for the occurrence of total internal reflection is that the angle of incidence is greater than the critical angle.

For visual demonstration purposes of total internal reflection one can use a body with a semicircular shape made out of glass. In this case there are only two options for the light beam. If the angle of incidence (θ) is smaller than the critical angle (θc), some of the rays will refract and leave the boundary while the others are reflected. On the other side, if the angle of incidence (θ) is greater than the critical angle (θc), the beam will be entirely reflected. At this point it is called total internal reflection.

For this phenomenon to appear, the angel of incidence needs to be above the critical angle. This specific angle should always reach 90°. This can be explained practically and theoretically by Snell’s Law. Practically one can explain the 90° by taking a light beam that travels from glass into air. By passing into a denser medium the ray is bent more towards the glass. When the incident angle becomes larger, the ray is more and more put into a horizontal position until it reaches 90°. Then there is no light that is transmitted into the air anymore.

The critical angle (θc) can also be pointed out by Snell’s law in theory, n1•sinθi = n2•sinθt. N1 and n2 are the refractive indices of the two mediums, which the light ray passes through. θi is the angle of incidence and θt is the angle of transmission. θi is equal to θc when θt= 90°. Therefore, sin •(90°)=1 and putting it into the formula it means n1•sinθi = n2. Afterwards the equation should be rearranged to sinθi = n2/ n1 and lastly to θi =sin-1 (n2/ n1). Considering the fraction (n2/ n1), the value of it has to be less than 1. This leads to the appearance of the total internal reflection. However, if (n2/ n1) is greater than 1, it is impossible to get a result of sin-1 and therefore there is no total internal reflection.

In conclusion, after getting an incidence with Snell’s law the critical angle always has to be 90°for an internal total reflection to appear. The angle of incidence has to be greater than the critical angle. Another condition for the occurrence of this phenomenon is that the light ray always has to pass from a medium of lower refractive index into a higher one. Total internal reflection is very common in Diamonds. It is one of the reasons why it has such a nice sparkle inside.

Sources:

Total internal reflection. (n.d.). Retrieved from http://www.physicsclassroom.com/class/refrn/u14l3b.cfm The critical angle. (n.d.). Retrieved from http://www.physicsclassroom.com/class/refrn/U14L3c.cfm Total internal reflection. (n.d.). Retrieved from http://en.wikipedia.org/wiki/Total_internal_reflection