Class 12/Notes/Wave Optics/eduPhysics
What Is Refraction of Light?
Refraction of light is the phenomenon in which light changes its direction of propagation when it passes obliquely from one transparent medium into another due to a change in its speed.
For example, a pencil partially immersed in a glass of water appears bent at the water surface. Similarly, the bottom of a swimming pool appears shallower than it actually is. These everyday observations are consequences of refraction.
Refraction occurs because light travels at different speeds in different optical media. When light enters a new medium at an angle other than 90° to the boundary, the change in speed generally changes its direction of propagation.
However, when light enters the second medium normally, its speed changes but its direction of propagation remains unchanged.
Why Does Light Change Direction During Refraction?
The direction of light changes during refraction because its speed changes when it passes from one optical medium to another at an oblique angle.
According to Huygens’ wave theory, every point on a wavefront acts as a source of secondary wavelets. The new wavefront is formed by the common envelope of these secondary wavelets.
Consider a plane wavefront travelling from air into glass obliquely. The portion of the wavefront that enters the glass first slows down, while the remaining portion is still travelling faster in air. As a result, the wavefront changes its orientation. Since light rays are perpendicular to the wavefronts, the direction of the rays also changes.
- From a rarer medium to a denser medium: When light enters a medium in which it travels more slowly, such as from air into glass, it bends towards the normal.
- From a denser medium to a rarer medium: When light enters a medium in which it travels faster, such as from glass into air, it bends away from the normal.
These statements describe the usual case of oblique incidence. At normal incidence, light changes speed without bending.
This wave-based explanation forms the foundation for deriving the laws of refraction using Huygens’ principle.
The direction of light changes during refraction because its speed changes when it passes from one optical medium to another at an oblique angle.
According to Huygens’ wave theory, every point on a wavefront acts as a source of secondary wavelets. The new wavefront is formed by the common envelope of these secondary wavelets.
Consider a plane wavefront travelling from air into glass obliquely. The portion of the wavefront that enters the glass first slows down, while the remaining portion is still travelling faster in air. As a result, the wavefront changes its orientation. Since light rays are perpendicular to the wavefronts, the direction of the rays also changes.
- From a rarer medium to a denser medium: When light enters a medium in which it travels more slowly, such as from air into glass, it bends towards the normal.
- From a denser medium to a rarer medium: When light enters a medium in which it travels faster, such as from glass into air, it bends away from the normal.
These statements describe the usual case of oblique incidence. At normal incidence, light changes speed without bending.
This wave-based explanation forms the foundation for deriving the laws of refraction using Huygens’ principle.
Important Terms Used in Refraction
To understand the laws of refraction and their derivation using Huygens’ wave theory, it is essential to understand the following terms.
Incident Ray, Refracted Ray and Normal
Incident ray: The ray of light that approaches the boundary separating two transparent media is called the incident ray.
Refracted ray: The ray that enters the second medium and continues its propagation after crossing the boundary is called the refracted ray.
Normal: The normal is an imaginary line drawn perpendicular to the boundary between the two media at the point where the incident ray strikes it. It serves as the reference line for measuring the angles of incidence and refraction.
The incident ray, refracted ray and normal are important elements in a refraction diagram. Both angles are measured with respect to the normal, not with respect to the surface.
Angle of Incidence and Angle of Refraction
Angle of incidence (i): The angle between the incident ray and the normal at the point of incidence is called the angle of incidence.
Angle of refraction (r): The angle between the refracted ray and the normal at the point of refraction is called the angle of refraction.
When light travels from air into glass at an oblique angle, the refracted ray bends towards the normal, so the angle of refraction is smaller than the angle of incidence. When light travels from glass into air under suitable conditions for refraction, it bends away from the normal, so the angle of refraction is greater than the angle of incidence.
These angles are related by Snell’s law:
n₁ sin i = n₂ sin r
where:
- n₁ is the refractive index of the first medium.
- n₂ is the refractive index of the second medium.
- i is the angle of incidence.
- r is the angle of refraction.
This relationship is one of the fundamental laws of geometrical optics and can be derived using Huygens’ wave theory.
Optical Density and Refractive Index
Optical density describes how strongly a medium affects the propagation speed of light compared with another medium. A medium in which light travels more slowly is optically denser than a medium in which light travels faster, for the same wavelength comparison under the usual school-level treatment.
Optical density should not be confused with mass density. A material with greater mass density does not necessarily have a greater refractive index.
Refractive index is a physical quantity that indicates how much the speed of light is reduced in a medium compared with its speed in vacuum.
The absolute refractive index of a medium is given by:
n = c/v
where:
- n is the absolute refractive index of the medium.
- c is the speed of light in vacuum.
- v is the speed of light in the medium.
Since the speed of light in a transparent medium is generally less than its speed in vacuum, its absolute refractive index is usually greater than 1.
For two transparent media, the relative refractive index of medium 2 with respect to medium 1 is:
n₂₁ = n₂/n₁ = v₁/v₂
where v₁ and v₂ are the speeds of light in media 1 and 2, respectively.
A higher refractive index generally corresponds to a lower speed of light in the medium. When light crosses a boundary, its frequency remains constant, while its speed and wavelength change.
This relationship between refractive index and the speed of light is essential for understanding why light bends at the boundary between two media and for deriving Snell’s law from Huygens’ wave theory.
1. Geometric Construction & Definitions
Interface (XY): A plane refracting surface separating two transparent media.
Medium 1 (Rarer Medium): Wave velocity is v1.
Medium 2 (Denser Medium): Wave velocity is v2, where v2 < v1.
AB (Incident Wavefront): A plane wavefront traveling obliquely toward the surface XY.
CD (Refracted Wavefront): The corresponding refracted wavefront in the second medium.
Angles:
- i = Angle of incidence
- r = Angle of refraction
2. Derivation of Wave Propagation Time
When the ray at point B reaches the boundary at point C in a given time t, the distance traveled by the incident wave is: BC = v1 * t
During this exact time interval t, secondary wavelets originating from point A travel into the second medium (denser medium) and cover a distance: AD = v2 * t
3. Mathematical Proof of Snell’s Law
From the right-angled triangle ABC: sin(i) = BC / AC = (v1 * t) / AC
From the right-angled triangle ADC: sin(r) = AD / AC = (v2 * t) / AC
Taking the ratio of sin(i) to sin(r): sin(i) / sin(r) = [(v1 * t) / AC] / [(v2 * t) / AC] = v1 / v2
Since velocities v1 and v2 in the respective media are constant, the ratio v1 / v2 equals a constant value known as the refractive index (n21) of the second medium with respect to the first medium: sin(i) / sin(r) = n21
This completes the theoretical proof of Snell’s Law of Refraction.
4. Verification of the Laws of Refraction
First Law: The incident wavefront (AB), the refracted wavefront (CD), and the normal to the refracting surface all lie in the same plane.
Second Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media (n21), verifying Snell’s law.
Leave a Reply