Factors affecting the angle of deviation

We know that a prism is an optical equipment which changes the direction of light that falls on it.

The image shows a ray of white light incident on a prism that undergoes deviation (change of direction).

The extent of deviation depends on factors that are related to the prism and the light itself.

Before discussing the factors affecting the angle of deviation, let us introduce an equation first.

The mathematical relation between the angle of incidence $i_1$, the angle of emergence $i_2$, the angle of the prism $A$ and the angle of deviation $\delta$ is $i_1+i_2=A+\delta$

Now, we will list down all the factors that affect the angle of deviation and briefly explore each one of them.

Let's begin with the first factor.

1. Angle of deviation, $\delta$, is dependent on the angle of incidence, $i_1.$

Experimental observation tells that if we increase $i_1$, the corresponding $\delta$ will first decrease until it attains a minimum value ${\delta }_m$. Further increasing $i_1$ will increase $\delta .$

The graph between $\delta$ and $i_1$ is plotted above. The value of $i_1$ for which $\delta \to {\delta }_m$ is labeled .

The situation $\delta \to {\delta }_m$ occurs when $\to i_1=i_2$, i.e. the angle of incidence and the angle of emergence are equal, or, $\to r_1=r_2$ i.e. the angles of refraction are equal.

If $i_1=i_2=i$, then equation ${i}_1+i_2=A+\delta$, gives ${\delta }_m=2i-A$ $\because \delta \to {\delta }_m\text{when}{i}_1=i_2$

It is interesting to note that this particular value of ${\delta }_m$ is unique for a particular glass prism and a particular colour of light.

This is because, for different colours, the angle of incidence $i_1$ corresponding to ${\delta }_m$ will be different.

So different $i_1$ will consequently give different ${\delta }_m.$

Let us look at the second factor now.

2. In addition to the angle of incidence, the angle of deviation, $\delta$, also depends on the refractive index, $\mu$, of the medium.

The dependence of $\delta$ on $\mu$ is linear as $\delta \propto \mu$ This means, denser the medium, greater will be the angle of deviation and vice versa.

Let us look at the third factor.

3. $\delta$ is also dependent on the angle of the prism $A$ i.e. $\delta \propto A$

This simply means that if the angle of the prism is large, the angle of deviation is large too and vice versa.

Finally, let us look at the fourth factor.

4. Lastly, $\delta$ also depends on the wavelength of the light ($\lambda$) used and is inversely proportional to the wavelength, i.e. $\delta \propto \frac{1}{\lambda }$

This means, more the value of the wavelength, less will be the angle of deviation and vice versa.

If we compare red and violet colours, ${\lambda }_{red}>{\lambda }_{violet}$ consequently, ${\delta }_{violet}>{\delta }_{red}$

So, violet deviates the most and red deviates the least. Other colours are in the intermediate positions.

Revision

The angle of deviation depends on the angle of incidence and the relation between them is described by this curve.

When the angle of incidence and emergence are the same we get a minimum deviation given by ${\delta }_m=2i-A$

Angle of deviation, $\delta$, is dependent on the angle of incidence, $i_1.$

The angle of deviation, $\delta$, also depends on the refractive index, $\mu$, of the medium.

$\delta$ is dependent on the angle of the prism $A.$

Lastly, $\delta$ also depends on the wavelength of the light($\lambda$) used and is inversely proportional to it.

The end