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What is total internal reflection?

Class 12 PhysicsNCERT chapter: Ray Optics and Optical Instrumentsइसे हिंदी में पढ़ें

Exam-ready answer

Total internal reflection is the complete reflection of light back into the same medium when light travels from an optically denser medium to a rarer medium and the angle of incidence is greater than the critical angle. No light is refracted. The critical angle is given by sin ic = 1/n; for glass in air it is about 42°.

Explanation

When a ray goes from glass into air, it bends away from the normal, so the angle of refraction r is larger than the angle of incidence i. A small part of the light is also reflected. As i increases, r increases faster. At one particular angle of incidence, called the critical angle ic, the refracted ray grazes along the surface (r = 90°).

If i is made larger than ic, refraction is no longer possible and all the light is reflected back into the denser medium. Since no part escapes by refraction, this is called total internal reflection. Putting r = 90° in Snell's law, n₁ sin ic = n₂ sin 90°, gives sin ic = n₂/n₁. For glass (n ≈ 1.5) in air, ic ≈ 42°; for water (n ≈ 1.33), ic ≈ 49°.

Both conditions must hold: light must travel from a denser to a rarer medium, and the angle of incidence must exceed the critical angle. Applications: diamonds sparkle because their small critical angle (about 24°) traps light by repeated total internal reflection; right-angled prisms bend light by 90° or 180° in periscopes and binoculars; optical fibres carry light signals over long distances. Mirages in deserts are also explained by it.

Points to remember

  1. Condition 1: light travels from an optically denser medium to a rarer medium.
  2. Condition 2: the angle of incidence is greater than the critical angle.
  3. Critical angle: the angle of incidence in the denser medium for which the angle of refraction is 90°.
  4. sin ic = 1/n, where n is the refractive index of the denser medium relative to the rarer medium (n ≈ 1.5 for glass in air).
  5. Applications: optical fibres, sparkling of diamond, totally reflecting prisms and mirage.

Exam tip

Draw three ray diagrams: i < ic, i = ic (refracted ray along the surface) and i > ic (total reflection). State both conditions and derive sin ic = 1/n from Snell's law with r = 90°.

Questions students also ask

Why does a diamond sparkle?
Diamond has a high refractive index (about 2.42), so its critical angle is only about 24°. Diamonds are cut so that light entering them suffers total internal reflection many times at the faces before leaving. The light comes out brightly from a few directions, so the diamond sparkles.
How do optical fibres use total internal reflection?
An optical fibre has a thin glass or plastic core surrounded by cladding of lower refractive index. Light entering one end strikes the core–cladding boundary at angles greater than the critical angle, so it is totally reflected again and again and travels along the fibre with very little loss, even when the fibre bends.
Can total internal reflection happen when light goes from air to glass?
No. When light goes from a rarer to a denser medium, it bends towards the normal, so the angle of refraction is always smaller than the angle of incidence. A refracted ray always exists, so total internal reflection is impossible in this direction.

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