Refraction of Light
2.0 Laws of refraction
2.0 Laws of refraction
There are two laws of refraction.
1. The incident ray, the normal and the refracted ray all lie in the same plane.
2. For any medium, the product of refractive index $\left( \mu \right)$ and angle which the light ray makes with the normal is constant. This is known as Snell's law.
Mathematically it can be written as, $$\mu \sin i = {\text{constant}}$$
For the following situation as shown in the figure, we can write Snell's law as,
$${\mu _1}\sin i = {\mu _2}\sin r = {\mu _1}\sin t$$ or $$\frac{{\sin i}}{{\sin r}} = \frac{{{\mu _2}}}{{{\mu _1}}}$$
As we know $\left( {\mu \propto \frac{1}{v}{\text{ and }}\mu \propto \frac{1}{\lambda }} \right)$
So, $$\frac{{\sin i}}{{\sin r}} = \frac{{{\mu _2}}}{{{\mu _1}}} = \frac{{{v_1}}}{{{v_2}}} = \frac{{{\lambda _1}}}{{{\lambda _2}}}$$
2.0.1 When light travels from rarer medium to denser medium
When the light travels from rarer medium to denser medium. So, we can write,
$${v_1} > {v_2}$$ and $${\mu _2} > {\mu _1}$$
As we know,
$$\frac{{\sin i}}{{\sin r}} = \frac{{{\mu _2}}}{{{\mu _1}}}$$
or
$$\frac{{\sin i}}{{\sin r}} > 1$$ So, $$i > r$$
The above equation suggests that the light ray bend towards the normal after refraction.
2.0.2 When light travels from denser medium to rarer medium
When the light travels from denser medium to rarer medium. So, we can write,
$${v_1} < {v_2}$$ and $${\mu _1} > {\mu _2}$$
As we know,
$$\frac{{\sin i}}{{\sin r}} = \frac{{{\mu _2}}}{{{\mu _1}}}$$
or
$$\frac{{\sin i}}{{\sin r}} < 1$$ So, $$i < r$$
The above equation suggests that the light ray bend away from the normal after refraction.
2.0.3 Combination of medium
Using Snell's law we can write,
$${\mu _1}\sin {i_1} = {\mu _2}\sin {i_2} = {\mu _3}\sin {i_3} = {\mu _4}\sin {i_4} = {\mu _1}\sin {i_5}$$
So, $${\mu _1}\sin {i_1} = {\mu _1}\sin {i_5}$$ Therefore, $${i_1} = {i_5}$$
So, the above experiment shows that if the boundaries of the media are parallel, then the emergent ray $CD$ is parallel to the incident ray $AB$, however they are laterally displaced.
