Table of Contents
Reflection, Refraction and Dispersion
1. Introduction
When light interacts with surfaces and transparent materials, it can change direction, speed or wavelength distribution. Three fundamental optical phenomena are reflection, refraction and dispersion.
These phenomena explain the formation of images in mirrors, the bending of light in water, the operation of lenses, the separation of white light into colours and many natural optical effects.
Understanding these principles is essential for studying geometrical optics and modern optical instruments.
2. Reflection of Light
2.1 Definition
Reflection is the phenomenon in which light strikes a surface and returns into the original medium.
It occurs when light interacts with a boundary between two materials.
Examples include:
- Images formed by mirrors
- Reflection from polished metal
- Light reflected from water
- Reflection from walls and other surfaces
2.2 Laws of Reflection
Reflection follows two fundamental laws.
First law: The incident ray, reflected ray and normal at the point of incidence all lie in the same plane.
Second law: The angle of reflection is equal to the angle of incidence.
[
\theta_i=\theta_r
]
Where:
- (\theta_i) = Angle of incidence
- (\theta_r) = Angle of reflection
Both angles are measured from the normal, which is an imaginary line perpendicular to the reflecting surface.
2.3 Regular Reflection
Regular reflection occurs when parallel light rays strike a smooth surface and are reflected in a regular, orderly manner.
Examples include:
- Plane mirrors
- Polished metal
- Calm water
It produces clear images when the reflecting surface is sufficiently smooth.
2.4 Diffuse Reflection
Diffuse reflection occurs when parallel incident rays strike a rough surface and are reflected in different directions.
Examples include:
- Paper
- Walls
- Unpolished wood
- Rough roads
Diffuse reflection allows objects to be seen from different directions, even though it does not normally produce a clear mirror image.
Importantly, the laws of reflection apply to individual rays at each point on a rough surface.
3. Plane Mirrors
A plane mirror has a flat reflecting surface.
3.1 Characteristics of Images
The image formed by a plane mirror is:
- Virtual
- Erect
- The same size as the object
- Laterally inverted
- Located as far behind the mirror as the object is in front of it
The image distance is equal to the object distance:
[
d_i=d_o
]
3.2 Lateral Inversion
Lateral inversion refers to the apparent reversal of left and right in a plane mirror.
For example, when a person raises the right hand, the image appears to raise the left hand.
The image is not actually rotated in the ordinary physical sense. The apparent reversal results from the way the reflected image is interpreted relative to the observer.
4. Refraction of Light
4.1 Definition
Refraction is the change in direction of light when it passes obliquely from one transparent medium into another because its speed changes.
For example, light changes speed when it travels from air into water or glass.
If light enters a medium with a higher refractive index at an angle, it bends towards the normal.
If it enters a medium with a lower refractive index, it bends away from the normal.
When light travels along the normal, its speed and wavelength change at the boundary, but its direction does not.
4.2 Refractive Index
The absolute refractive index of a medium is defined as:
[
n=\frac{c}{v}
]
Where:
- (n) = Refractive index
- (c) = Speed of light in vacuum
- (v) = Speed of light in the medium
The refractive index is dimensionless.
A higher refractive index means that light travels more slowly in the material under the relevant conditions.
4.3 Relative Refractive Index
The refractive index of medium 2 relative to medium 1 is:
[
n_{21}=\frac{v_1}{v_2}
]
For non-magnetic optical media under ordinary conditions, this can also be expressed using their absolute refractive indices:
[
n_{21}=\frac{n_2}{n_1}
]
5. Snell’s Law
Snell’s law describes the relationship between the angles of incidence and refraction.
[
n_1\sin\theta_1=n_2\sin\theta_2
]
Where:
- (n_1) = Refractive index of the first medium
- (n_2) = Refractive index of the second medium
- (\theta_1) = Angle of incidence
- (\theta_2) = Angle of refraction
The angles are measured from the normal to the boundary.
5.1 Bending Towards the Normal
When light passes from a medium of lower refractive index to one of higher refractive index, it bends towards the normal, provided it is incident obliquely.
Example: Light travelling from air into glass.
5.2 Bending Away from the Normal
When light passes from a medium of higher refractive index to one of lower refractive index, it bends away from the normal.
Example: Light travelling from glass into air.
5.3 No Change in Direction
When light strikes a boundary normally, its direction remains unchanged even though its speed and wavelength may change.
6. Apparent Depth
An object submerged in water appears closer to the surface than its actual depth.
This is due to refraction at the water-air boundary.
For near-normal viewing through a flat surface:
[
\text{Refractive index}=
\frac{\text{Real depth}}{\text{Apparent depth}}
]
Therefore:
[
d_a=\frac{d_r}{n}
]
Where:
- (d_a) = Apparent depth
- (d_r) = Real depth
- (n) = Refractive index of the medium relative to the viewing medium
This relation is an approximation for near-normal observation through a plane boundary.
7. Total Internal Reflection
7.1 Definition
Total internal reflection occurs when light travelling from an optically denser medium to an optically rarer medium strikes the boundary at an angle greater than the critical angle.
Under these conditions, the light is reflected completely back into the denser medium.
Two conditions are necessary:
- Light must travel from a medium of higher refractive index to one of lower refractive index.
- The angle of incidence must exceed the critical angle.
7.2 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.
For light travelling from medium 1 to medium 2, where (n_1>n_2):
[
\sin C=\frac{n_2}{n_1}
]
Where (C) is the critical angle.
If the second medium is air and the first medium has refractive index (n):
[
\sin C=\frac{1}{n}
]
7.3 Applications of Total Internal Reflection
A. Optical Fibres
Optical fibres transmit light through repeated total internal reflection within a high-refractive-index core surrounded by lower-refractive-index cladding.
B. Medical Endoscopes
Optical fibres carry light and images through flexible instruments used for examining internal body structures.
C. Prisms
Prisms can use total internal reflection to change the direction of light efficiently.
D. Reflectors
Certain optical reflectors use total internal reflection to redirect light.
E. Natural Optical Effects
The brilliance of diamonds is partly associated with their high refractive index and the resulting optical behaviour, including total internal reflection.
8. Dispersion of Light
8.1 Definition
Dispersion is the separation of light into its component wavelengths when it passes through a refracting medium because the refractive index depends on wavelength.
A triangular glass prism can separate white light into a spectrum of colours.
8.2 Formation of a Spectrum
White light contains a range of visible wavelengths.
When it enters a dispersive material, different wavelengths experience different refractive indices and are refracted by different amounts.
In ordinary glass under normal visible-light conditions:
- Violet light generally deviates more.
- Red light generally deviates less.
This produces the visible spectrum.
8.3 Order of Colours
The commonly recognized order of the visible spectrum is:
Violet, Indigo, Blue, Green, Yellow, Orange and Red.
Violet generally has the shortest visible wavelength, while red has the longest.
8.4 Cause of Dispersion
The refractive index of many transparent materials varies with wavelength.
This phenomenon is called material dispersion.
The variation in refractive index causes different colours to travel at different speeds inside the material and therefore to refract by different amounts.
8.5 Rainbow Formation
A rainbow is produced through the interaction of sunlight with water droplets in the atmosphere.
The main optical processes are:
- Refraction as sunlight enters a droplet.
- Dispersion, which separates the different wavelengths.
- Internal reflection inside the droplet.
- Refraction as light leaves the droplet.
A primary rainbow has red on its outer edge and violet on its inner edge.
A secondary rainbow is generally fainter and has reversed colour order because of two internal reflections.
9. Atmospheric Refraction
Atmospheric refraction occurs when light travels through layers of air with different densities and refractive indices.
The refractive index of air generally varies with temperature, pressure and composition.
Examples include:
- Apparent early sunrise
- Apparent delayed sunset
- Twinkling of stars
- Atmospheric mirages
9.1 Twinkling of Stars
Starlight passes through constantly changing atmospheric layers.
Variations in air density cause changes in the path of light, making the apparent position and brightness of stars fluctuate.
This effect is called atmospheric scintillation.
Planets usually twinkle less noticeably because they appear as extended sources rather than nearly point-like sources.
9.2 Mirage
A mirage is an optical phenomenon caused by the bending of light through layers of air with varying refractive indices.
A common example is the appearance of water-like reflections on a hot road.
The phenomenon is not necessarily caused by actual water on the road.
10. Optical Scattering
Scattering is the redirection of light by particles or irregularities in a medium.
10.1 Rayleigh Scattering
Rayleigh scattering occurs when the scattering particles are much smaller than the wavelength of light.
For ideal small particles, the scattering intensity is approximately proportional to:
[
I_s\propto\frac{1}{\lambda^4}
]
Shorter wavelengths are scattered more strongly than longer wavelengths.
This explains why the daytime sky appears blue.
10.2 Why Does the Sky Appear Blue?
Molecules in the atmosphere scatter shorter wavelengths of sunlight more strongly than longer wavelengths.
Blue light is therefore scattered in many directions and reaches the observer from across the sky.
10.3 Why Are Sunsets Red?
At sunrise and sunset, sunlight travels through a longer path in the atmosphere.
Much of the shorter-wavelength light is scattered out of the direct path, allowing more red and orange light to reach the observer.
Dust, aerosols and atmospheric conditions can also influence sunset colours.
11. Worked Numerical Examples
Example 1: Refraction Through Glass
A ray of light travels from air into glass. The angle of incidence is 30 degrees and the refractive index of glass is 1.5. Find the angle of refraction, assuming the refractive index of air is approximately 1.
Using Snell’s law:
[
n_1\sin\theta_1=n_2\sin\theta_2
]
[
1\times\sin30^\circ=1.5\sin\theta_2
]
[
0.5=1.5\sin\theta_2
]
[
\sin\theta_2=\frac{0.5}{1.5}
]
[
\theta_2=\sin^{-1}(0.3333)
]
[
\boxed{\theta_2\approx19.5^\circ}
]
The ray bends towards the normal.
Example 2: Critical Angle
Calculate the critical angle for a glass-air boundary when the refractive index of glass is 1.5.
[
\sin C=\frac{1}{1.5}
]
[
C=\sin^{-1}(0.6667)
]
[
\boxed{C\approx41.8^\circ}
]
Example 3: Apparent Depth
A swimming pool is 2.4 metres deep. If the refractive index of water is 1.33, calculate its apparent depth when viewed nearly vertically from air.
[
d_a=\frac{d_r}{n}
]
[
d_a=\frac{2.4}{1.33}
]
[
\boxed{d_a\approx1.80\ m}
]
The pool appears shallower than its actual depth.
12. Common Examination Misconceptions
- Angles of incidence and reflection are measured from the normal, not from the surface.
- The laws of reflection apply to both regular and diffuse reflection.
- Refraction occurs because the speed of light changes between media.
- Frequency remains constant during ordinary refraction at a stationary boundary.
- Light bends towards the normal when it enters a higher-index medium obliquely.
- Total internal reflection is possible only when light travels from higher to lower refractive index.
- The angle of incidence must exceed the critical angle for total internal reflection.
- Dispersion occurs because refractive index depends on wavelength.
- Violet light generally deviates more than red light in ordinary glass.
- The primary rainbow has red on the outside and violet on the inside.
36 Key Takeaways for Exams
- Reflection is the return of light into its original medium after striking a surface.
- The first law of reflection states that the incident ray, reflected ray and normal lie in the same plane.
- The second law of reflection states that the angle of incidence equals the angle of reflection.
- Angles of incidence and reflection are measured from the normal.
- Regular reflection occurs from smooth surfaces.
- Diffuse reflection occurs from rough surfaces.
- A plane mirror forms a virtual and erect image.
- A plane mirror produces an image equal in size to the object.
- The image distance in a plane mirror equals the object distance.
- Lateral inversion is the apparent reversal of left and right.
- Refraction is the change in direction of light due to a change in speed between media.
- The absolute refractive index is (n=c/v).
- Refractive index is a dimensionless quantity.
- Snell’s law is (n_1\sin\theta_1=n_2\sin\theta_2).
- Light bends towards the normal when entering a higher-index medium obliquely.
- Light bends away from the normal when entering a lower-index medium obliquely.
- Light travelling normally across a boundary does not change direction.
- Frequency remains unchanged during ordinary refraction at a stationary boundary.
- Apparent depth is generally less than real depth when an object is viewed underwater from air.
- Total internal reflection occurs when light travels from a higher-index medium to a lower-index medium at an angle exceeding the critical angle.
- The critical angle satisfies (\sin C=n_2/n_1) when (n_1>n_2).
- Optical fibres use total internal reflection.
- Endoscopes use optical fibres to examine internal body structures.
- Dispersion is the separation of light into component wavelengths.
- A glass prism can separate white light into a visible spectrum.
- Violet light generally deviates more than red light in ordinary glass.
- Red light generally has the longest visible wavelength.
- A primary rainbow is formed through refraction, dispersion and internal reflection in water droplets.
- A secondary rainbow generally has reversed colour order compared with a primary rainbow.
- Atmospheric refraction causes apparent changes in the position of celestial objects.
- Twinkling of stars is associated with atmospheric scintillation.
- Mirages result from refraction through layers of air with varying refractive indices.
- Rayleigh scattering is stronger for shorter wavelengths.
- Rayleigh scattering helps explain the blue appearance of the daytime sky.
- Red and orange colours often dominate sunsets because shorter wavelengths are scattered out of the direct sunlight path.
- Reflection, refraction and dispersion are fundamental phenomena underlying many optical devices and natural visual effects.