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Karnataka Board PUCPUC Science 2nd PUC Class 12

Refraction at a Rarer Medium

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Estimated time: 7 minutes
CBSE: Class 12

Introduction

When light travels from an optically denser medium to an optically rarer medium, its speed increases in the second medium and the refracted ray bends away from the normal.

For refraction between two media, Snell’s law is: n1​sin i = n2​sin r

For denser to rarer transition, n1 > n2, so the refracted angle is greater than the angle of incidence.

CBSE: Class 12

Definition: Rarer Medium

A rarer medium is a medium in which light travels faster and whose refractive index is lower compared with the denser medium.

CBSE: Class 12

Definition: Critical Angle

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes 90 degrees.

If i = ic, then the refracted ray travels along the boundary surface.

CBSE: Class 12

Definition: Total Internal Reflection

Total internal reflection is the complete reflection of light back into the denser medium when light travels from a denser to a rarer medium, and the angle of incidence becomes greater than the critical angle.

CBSE: Class 12

Derivation of critical angle

At the critical angle,

  • angle of incidence = ic
  • angle of refraction = 90°.

Using Snell’s law,

n1sin ic = n2 sin ⁡90

Since sin⁡ 90 = 1,

n1 sin ⁡ic = n2

Therefore,

sin⁡ ic = \[\frac {n_2}{n_1}\]
CBSE: Class 12

Condition flow

Condition Result Meaning
(i < ic) Refraction occurs Light passes from the denser medium into the rarer medium.
(i = ic) r = 90° The refracted ray grazes along the surface.
(i > ic) Total Internal Reflection (TIR) No refracted ray enters the rarer medium; the light is completely reflected back into the denser medium.

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