Question

Explain the phenomenon of total internal reflection derive the relation between critical angle and refractive index of the medium

Answer 1

$\bold{TOTAL \: INTERNAL \: REFLECTION}$

The total reflection of the light into the same medium after reflection, when light travels from denser medium to rarer medium and the angle of incidence is greater than critical angle is called total internal reflection.

◼For total internal reflection light must :-

▶Travel from denser to rarer medium .

▶The angle of incidence should be greater than critical angle.

$\bold{CRITICAL \: ANGLE}$

When the light travels from denser medium to rarer medium and the angle of incidence for denser medium is such that the angle of refraction in rarer medium becomes 90 degrees, is called critical angle.

$\bold{RELATIONSHIP \: BETWEEN \:}$$\bold{REFRACTIVE \: INDEX \:AND \: CRITICAL \: ANGLE}$

When the light travels from air to glass

let the angle of incidence be i and critical angle be c.

When the angle of refraction is 90 , i = c .

We know,

$\boxed{Refractive \: index = \dfrac{sin \: i}{sin \:r}}$

So,

$Refractive \: index = \dfrac{sin \: C}{sin 90^{\circ}}$

Since,

$\boxed{sin \: 90^{\circ} = 1}$

So,

$Refractive \: index\: glass \: with \: water= \dfrac{1}{Refractive \: index\: water \: with \: glass}$

So,

$Refractive \: index\: glass \: with \: water= \dfrac{1}{sin \: c}$

Since,

$\boxed{\dfrac{1}{sin \: c}= cosec \:c}$

$\large \boxed{Refractive \: index\: glass \: with \: water= cosec \: c}$