Some Standard Conceptual Questions on TIR

We all see the phenomena of total internal reflection of light in our daily life.

For example, the formation of a mirage in deserts.

And the sparkling of the diamond is also the phenomena of total internal reflection.

Total internal reflection is the reflection of light which occurs when the light strikes the interface at the interface of the media.

And the angle of incidence is greater than the critical angle for the pair of media.

Now, we will discuss some conceptual question on total internal reflection.

Let's take a question on total internal reflection.

Suppose a light is traveling from diamond to the silicon.

Now, we need to find when the light will undergo total internal reflection.

As the index of refraction of the diamond is $3$.

And the index of the refraction of the silicon is $4$.

So, the light will never undergo a total internal reflection.

Because, there are two conditions of total internal reflection.

First one is the light must be passed through the denser medium to rarer medium.

And the second one is the angle of incidence should be greater than the critical angle.

Since, here diamond is the rarer medium, So, there will be never the condition of total reflection.

Let's take a problem based on the total internal reflection.

Suppose, we have a optical wire with a light beam travelling through it.

And it is surrounded by a liquid with a refractive index of $1.30$.

The refractive index of the wire is $1.80$.

Now, we need to find the critical angle needed to achieve the total internal reflection.

As the condition of total internal reflection occurs, when the refracted will bend by $90°$ from the normal.

Then, the angle of incidence is called critical angle.

Hence, from Snell's law,

From the question,

Now, after putting these values in the equation, we get

Hence, at the angle of $45.97°$, the light will be reflected at the $90°$ from the normal.

Hence, the angle of $45.97°$ is the critical angle for the light.

The End