Question

What is meant by critical angle for a given refracting medium? Establish a relationship between critical angle and refractive index. What is a total internal reflection, and when does it take place?

Accepted Answer

When a ray of light enters from a denser medium to a rarer medium, the diffracted ray turns away from the normal. The critical angle is the angle of incidence for which the angle of refraction is $90 °$ . If the incident angle exceeds this value, the ray is reflected back into the denser medium. This is called total internal reflection.

In such case incident angle $i = C (C r i t i c a l a n g l e), r = 90 °,$ $μ_{a}$ = refractive index of the rarer medium

$μ_{b}$ =refractive index of the denser medium

Applying Snell's law,

$\frac{\sin i}{sir r} = \frac{μ_{a}}{μ_{b}} = \frac{\sin C}{\sin 90}$

Substituting these values, we have,

$μ_{b} \sin C = μ_{a} \sin 90$

Or $\frac{\sin C}{sir 90} = \frac{μ_{b}}{μ_{a}} or \frac{μ_{b}}{μ_{a}} = \frac{1}{\sin C}$

Let consider a light from an object O in the denser medium is passing through a rarer medium as shown in the figure. The ray $OA$ will pass through ${AB}_{1}$ following the laws of refraction. The other rays incident at different angle of incidence will similarly follow the path. ${OB}_{2,} {OB}_{3} etc .$ If the angle of incidence become greater than a certain value (called critical angle)The ray will reflected back to the first medium and no portion of the light beyond this critical value will pass through the second medium, This is called Total Internal Reflection

Thus Total internal reflection is the phenomenon of reflection of light into a denser medium from an interface of this denser medium and a rarer medium.

The essential conditions for the total internal refection are :

(1)The light should travel from denser medium to rarer medium

(2) The angle of incidence in the denser medium should be greater than the critical angle of the pair of media in contact

What is meant by critical angle for a given refracting medium? Establish a relationship between critical angle and refractive index. What is a total internal reflection, and when does it take place?

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