Revision: Optics (Ray and Wave Optics) >> Refraction of Light at a Plane Interface : Total Internal Reflection : Optical Fibre Physics (Theory) ISC (Science) ISC Class 12 CISCE

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

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Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

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The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.

The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.

Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.

Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

It is defined as the ratio of the velocity of light in medium 1 to the velocity of light in medium 2.

The perpendicular distance XY between the path of the emergent ray BC and the direction of the incident ray OD is called the lateral displacement.

Critical angle is the angle of incidence in the denser medium corresponding to which the angle of refraction in the rarer medium is 90°.

When a ray of light propagates from a denser medium to a rarer medium, the angle of incidence for which the angle of refraction is 90° is called the critical angle.

When a ray of light, travelling from a denser medium to a rarer medium, is incident at the interface of the two media at an angle greater than the critical angle for the two media, the ray is 'totally' reflected back into the denser medium.

The critical angle for two given media is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

“The perpendicular distance between the emergent ray and the direction of the incident ray is called the lateral shift.”

When the velocity of light in a medium is compared with that in another medium, the parameter is called the relative refractive index.

The refractive index of a medium is the parameter that tells how much slower light travels in that medium compared to vacuum.

Mathematically,
n = \[\frac{\text{velocity of light in vacuum}}{\text{velocity of light in medium}}=\frac{c}{v}\]

where c = 3 × 10⁸ ms^-1.

\[^1n_2=\frac{v_1}{v_2}=\frac{n_2}{n_1}\]

Lateral shift (d) = t sin (i − r) sec r

\[^2n_3=\frac{n_3}{n_2}\]

\[_1n_2=\frac{1}{\sin C}\cdot\]

Ray 2 shows partially reflected ray.

Statement

When a light ray, after undergoing any number of reflections and refractions, has its direction reversed, it retraces its entire original path. This is called the principle of reversibility of light.

Explanation / Proof

Consider a light ray passing from medium 1 to medium 2 and suffering refraction at the boundary.
Let the angle of incidence be i and the angle of refraction be r.

By Snell’s law, the refractive index of medium 2 with respect to medium 1 is:

¹n₂ = \[\frac {sin ⁡i}{sin⁡ r}\]​

Now, suppose the refracted ray is reflected back and retraces the path in the reverse direction. In this case, the angle of incidence becomes r, and the angle of refraction becomes i.

Again, by Snell’s law, the refractive index of medium 1 with respect to medium 2 is:

²n₁ = \[\frac {sin ⁡r}{sin ⁡i}\]​

Multiplying the two equations:

¹n₂ × ²n₁ = 1

This shows that the ray follows the same path in the reverse direction, proving the reversibility of the light path.

Conclusion

Hence, a light ray always retraces its original path when its direction is reversed, even after multiple reflections and refractions. This establishes the principle of reversibility of light.

• Refractive index indicates the direction of bending of light at a boundary (towards or away from the normal).
• It gives the ratio of the speeds of light in vacuum and in the medium:
  n = \[\frac {c}{v}\]So, a higher refractive index means a lower speed of light in the medium.
• The frequency of light remains unchanged during refraction, but the wavelength changes; hence, the refractive index also gives information about the wavelength of light in a medium.

• An object in a denser medium appears raised when viewed from a rarer medium due to refraction.
• Real depth is the actual depth of the object; apparent depth is the depth at which it appears.
• Refractive index is given by:
  n = \[\frac{\text{Real depth}}{\text{Apparent depth}}\]​
• Normal displacement is the difference between real and apparent depths:
  d = Real depth − Apparent depth
• For a medium of thickness t:
  d = t (1 − \[\frac {1}{n}\])

• Refraction occurs due to a change in the speed of light when it passes from one medium to another.
• The greater the change in speed, the greater is the bending of light at the boundary of the two media.
• According to Snell’s law:
  If v₁ > v₂​, the ray bends towards the normal (rarer to denser medium).
  If v₁ < v₂​, the ray bends away from the normal (denser to rarer medium).

• Mirage is caused by total internal reflection in hot air layers, making objects appear inverted, as in water reflections.
• Diamonds sparkle because light undergoes repeated total internal reflections due to their small critical angle.
• Totally reflecting prisms use total internal reflection to reflect light efficiently.
• Right-angled prisms can turn light by 90° or 180° using total internal reflection.
• Prisms are better than mirrors because they reflect almost all light and produce clear images.
• Optical fibres guide light by total internal reflection and are used in communication and medical imaging.