# Question 82804

May 18, 2016

See below.

#### Explanation:

Look at the following figure

It shows a ray of light traveling from a medium 1 to an optically different medium 2. The wave-front is depicted with help of parallel lines drawn perpendicular to the direction of motion of the ray. Angle of incident ray and the normal at the point of incidence is ${\theta}_{1}$ and angle of refracted ray and the normal at the same point is ${\theta}_{2}$. Notice the difference in spacing of wave-front lines in both media.

For quantitative analysis we redraw the figure as below where ray has been omitted for sake of simplicity.

Distance between the adjacent wave-front lines is wave length $\lambda$ and has been labelled appropriately.

Notice in this figure, ${1}^{s t} \text{ to } {7}^{t h}$ wave-fronts counted from the top, which are completely situated in the same medium which has low refractive index ${n}_{1}$.

We observe ${8}^{t h}$ wave-front line.

• The left part of the wave-front has hit and entered the medium $2$ of higher refractive index ${n}_{2}$ and
• Remaining part of the wave-front is still continuing its journey in medium $1$ which has low refractive index in both media.

Needless to say that this has happened only due to oblique incidence of the ray at the interface of the two media, angle being ${\theta}_{1}$.
Due to difference in refractive indices of two media, wave-front is distorted. The part of the wave-front which is in medium $1$ has wave length ${\lambda}_{1}$ and remaining part which has entered medium $2$ has wave length ${\lambda}_{2}$. Once the complete wave-front has crossed over to the denser medium, the distortion vanishes and ray of light proceeds ahead, bent at an angle ${\theta}_{2}$ as shown. For the case under discussion ${\theta}_{2} < {\theta}_{1}$.

Light travels at differently speeds in different media. At the interface, the wave front must change speed. In this case, a ray of light enters a high - refractive index material, the wave front will slow down

It shows that when a ray of light moves from an optically rarer to a denser medium, it is refracted towards the normal.

In this discussion we have respected the law of conservation of energy and assumed all the time frequency of the light ray remains same in both the media. ("Energy" E=hnu)#. However, due to the relation velocity $v = \nu \lambda$, velocities and respective wavelengths in two media are related as:
${v}_{1} / {\lambda}_{1} = {v}_{2} / {\lambda}_{2}$

The second part can be proved by reversing the direction of the ray of light and following the explanation above.
Now the refracted ray becomes the incident ray. It moves from an optically denser medium to a rarer medium. The incident ray becomes the refracted ray which is bent away from the normal.
-.-.-.-.-.-.-.-.-.-.-.-.

Snell's law, relation connecting the refractive indecies and the angles shown in the figure.

${n}_{1} \sin {\theta}_{1} = {n}_{2} \sin {\theta}_{2}$

Play and learn with this application.