Wavefront is defined as the locus of all the points in space that reach a particular distance by a propagating wave at the same instant.
A wave front is defined as a surface of constant phase.
Definition: Ray Optics
The branch of optics that is based on rectilinear propagation of light and deals with mirrors, lenses, reflection, refraction, etc. is called ray optics.
Definition: Wave Optics
The branch of optics that considers light as a wave which can bend around objects, diffract and interfere, etc. is called wave optics.
Definition: Electromagnetic Wave (Maxwell)
Coupled time-varying electric and magnetic fields that propagate in space are called electromagnetic waves.
Definition: Polarisation
The phenomenon that is based on the fact that light waves are transverse electromagnetic waves is called polarisation.
Definition: Wavefront
The locus of all those particles which are vibrating in the same phase at any instant is called a wavefront; thus a wavefront is a surface of constant phase.
Definition: Spherical Wavefront
When the source of light is a point source, the wavefront which is a sphere with the centre as the source is called a spherical wavefront.
Definition: Cylindrical Wavefront
When the source of light is linear and all the points equidistant from the source lie on a cylinder, the wavefront which is cylindrical in shape is called a cylindrical wavefront.
Definition: Wavelets
The secondary light waves emitted in all directions by each point on a wavefront, which travel with the speed of light in the medium, are called wavelets.
Definition: Plane Wavefront
When a point source or linear source of light is at very large distance and a small portion of the spherical or cylindrical wavefront appears to be plane, such a wavefront is called a plane wavefront.
Definition: Speed of Wave
The speed with which the wavefront moves outwards from the source is called the speed of wave.
Definition: Plane of Vibration
The plane in which E vibrates/oscillates is known as the plane of vibration.
Definition: Polaroid
A thin film of ultramicroscopic crystals used to produce plane polarised light is called a polaroid.
Definition: Unpolarised Wave
When the plane of vibration of a wave is changed randomly in very short intervals of time, such waves are called unpolarised waves.
Definition: Plane of Polarisation
The plane in which vibrations are present is called the plane of polarisation.
Definition: Polarisation of Light
The phenomenon of restriction of the vibration of light waves in a particular plane perpendicular to the direction of wave motion is called polarisation of light.
or
The phenomenon of confining the vibrations of the electric vector to a particular direction perpendicular to the direction of propagation of light is called Polarization.
Definition: Transverse Wave
When the displacement of the particle is perpendicular to the direction of propagation of the wave, then it is said to be transverse wave.
Definition: Linearly Polarised Wave (Plane Polarised Wave)
The wave in which the vibration of electric field vectors are confined in one plane and parallel to one unique direction is called linearly polarised wave; it is also referred to as plane polarised wave.
Definition: Wave Interference
The phenomenon that occurs when two waves meet while travelling along the same medium is called wave interference.
Definition: Destructive Interference
The points of minimum intensity in the regions of superposition of waves are said to be in destructive interference.
Definition: Constructive Interference
The points of maximum intensity in the regions of superposition of waves are said to be in constructive interference.
Definition: Interference of Light
The phenomenon of redistribution of energy on account of superposition of light waves from two coherent sources is called interference of light.
Definition: Fraunhofer Diffraction
The type of diffraction that occurs when the source and the observation screen are far away (effectively at infinite distance) from the diffracting object and fringes are not sharp and well-defined is called Fraunhofer diffraction.
Definition: Fresnel Diffraction
The type of diffraction that occurs when the source or screen is at a finite distance from the diffracting object and fringes are not sharp and well-defined is called Fresnel diffraction.
Definition: Diffraction of Light
The bending of light near the edge of an obstacle or slit and spreading into the region of geometrical shadow is called diffraction of light.
Definition: Resolving Power of Telescope
The reciprocal of the least angular separation between the objects that are just resolved is called the resolving power of the telescope.
Definition: Numerical Aperture (N.A.)
The quantity μ sin θ, where μμ is the refractive index of the medium between the object and the objective, is called the numerical aperture (N.A.) of the objective of the microscope.
Definition: Resolving Power of an Optical Instrument
The ability of an optical instrument to produce distinctly separate images of two objects very close to each other is called the resolving power of the instrument.
Definition: Limit of Resolution
The minimum distance of separation between two objects when they can be observed as separate by an optical instrument is called the limit of resolution of that instrument.
Definition: Resolving Power (Mathematical)
The reciprocal of the limit of resolution is called its resolving power.
Definition: Ray of Light
- The path along which light travels is called a ray of light.
- A ray is defined as the path of energy propagation in the limit of wavelength tending to zero.
Definition: Ray Optics or Geometrical Optics
- The study of optical phenomena under the assumption that it travels in a straight line as a ray is called ray optics or geometrical optics, as geometry is used in this study.
- The branch of optics in which one completely neglects the finiteness of the wavelength is called geometrical optics.
Definition: Fraunhofer Diffraction
Diffraction observed when the source and screen are at large distances from the diffracting element, so that the incident wavefront is plane.
Definition: Resolving Power of Telescope
The resolving power of a telescope is then defined as the reciprocal of the least angular separation between the objects that are just resolved.
Defintiion: Diffraction of Light
Diffraction of light is the phenomenon in which light spreads into the geometrical shadow region when it passes around the edges of an obstacle or through a narrow aperture whose size is comparable to its wavelength.
Definition: Wave Optics
The branch of optics which uses the wave nature of light to explain the optical phenomena is called wave optics.
Definition: Unpolarized Light
Light in which the electric field vectors vibrate in all possible directions perpendicular to the direction of propagation.
Definition: Plane Polarized Light
Light in which the electric field vectors vibrate only in one particular direction perpendicular to the direction of propagation.
Definition: Polarization by Scattering
Polarisation by scattering is the phenomenon in which unpolarized light becomes partially or completely plane polarised when it is scattered by small particles such as air molecules or dust particles.
Definition: Polarizer
A material that allows only those light waves to pass whose electric field is along a particular direction (polarizing axis).
Definition: Fresnel Diffraction
Diffraction observed when the source or screen (or both) are at finite distances from the obstacle, and the incident wavefront is spherical or cylindrical.
Definition: Plane of Polarization
The plane perpendicular to the plane of the vibration and the electric field vector is called plane of polarization.
Definition: Plane of Vibration
The plane containing the electric field vectors of plane polarized light is called the plane of vibration.
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 is 90°.
Definition: Interference
Interference is the phenomenon in which the intensity of light (or any wave) at a point becomes non-uniform due to the superposition of two or more coherent waves, resulting in regions of constructive and destructive interference.
Definition: Resolving Power
The ability of an optical instrument to distinguish two closely spaced objects as separate and distinct is called its resolving power.
Definition: Limit of Resolution
The minimum visual angle between two objects that can be just resolved by an instrument is called the limit of resolution.
Formula: Resultant Amplitude
When two waves of amplitudes a1 and a2 interfere at a point where phase difference is ϕ, the resultant amplitude is:
\[A^2=a_1^2+a_2^2+2a_1a_2\cos\phi\]
Formula: Resultant Intensity
I = I1 + I2 + 2\[\sqrt {I_1I_2}\] ⋅ cos ϕ
When I1 = I2 = I0:
I = \[2I_0(1+\cos\phi)=4I_0\cos^2\left(\frac{\phi}{2}\right)\]
Formula: Ratio of Maximum to Minimum Intensity
\[\frac{I_{\max}}{I_{\min}}=\left(\frac{a_1+a_2}{a_1-a_2}\right)^2=\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)^2\]
Formula: Resolving Power
R.P. = \[\frac {1}{\text {Limit of resolution}}\]
Formula: Resolving Power of Microscope
R.P. = \[\frac {1}{d}\] = \[\frac{2\mu\sin\theta}{\lambda}\]
where μ sin θ is the Numerical Aperture (N.A.) of the objective.
Formula: Resolving Power of Telescope
R.P. = \[\frac{1}{d\theta}=\frac{D}{1.22\lambda}\]
Formula: Critical Angle
\[
\sin C = \frac{n_2}{n_1}
\]
Where:
For air:
\[
\sin C = \frac{1}{\mu}
\]
Formula: Fraunhofer Diffraction at a Single Slit
\[a\sin\theta=\pm\left(n+\frac{1}{2}\right)\lambda\]
Formula: Width of the Central Bright Fringe
\[W_{c}=2y_{1d}=2W=2\left(\frac{\lambda D}{a}\right)\]
Law: Huygens' Principle
Huygens' Principle states that:
- Each point on a wavefront acts as a secondary source of light emitting secondary light waves called wavelets in all directions.
- These wavelets travel with the speed of light in the medium.
- The new wavefront can be obtained by taking the envelope of these secondary wavelets travelling in the forward direction.
- The wavelets travelling in the backward direction are ineffective.
Additional Points:
- Huygens' principle is a geometrical construction which gives the shape of the wavefront at any time and allows us to determine the shape of the wavefront at a later time.
- It also tells how a wavefront propagates through a medium.
- The energy of the wave travels in a direction perpendicular to the wavefront.
Law: Malus' Law
Statement: When plane polarised light is incident on an analyser, the resultant intensity of light transmitted from the analyser varies directly as the square of the cosine of the angle between the plane of transmission axis of the analyser and polariser.
Formula:
Where:
- I0 = intensity of plane polarised light
- I = intensity of transmitted light from the analyser
- θ = angle between the axis of the polariser and the analyser
Law: Young's Double Slit Experiment
Thomas Young first demonstrated the phenomenon of interference of light with the help of a slit, using a monochromatic source and two slits S1 and S2, producing alternating bright fringes (constructive interference) and dark fringes (destructive interference) on a screen.
Law: Malus’ Law
I2 = I1cos2θ
It gives the intensity of plane polarized light after passing through a second polarizer, where θ is the angle between the axes of the two polarizers.
Law: Brewster’s Law
Statement
When unpolarized light is incident on a transparent surface at a particular angle (called Brewster’s angle), the reflected light is completely plane polarised.
At this angle, the reflected and refracted rays are perpendicular to each other.
tanθB = \[\frac {n_2}{n_1}\]
where
θB = Brewster’s angle
n1, n2 = refractive indices of the two media
Proof
At Brewster’s angle,
θB + r = 90∘
From Snell’s law:
n1 sin θB = n2 sin r
Since r = 90∘ − θB,
n1 sinθB = n2 cosθB
tan θB = \[\frac {n_2}{n_1}\]
Conclusion
At Brewster’s angle, the reflected light is completely plane polarized and the reflected and refracted rays are mutually perpendicular.
Law: Rayleigh’s Criterion
According to Rayleigh’s criterion, two objects are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other.
Law: Laws of Reflection
First Law of Reflection:
i = r
The angle of incidence is equal to the angle of reflection.
Second Law of Reflection:
The incident ray, reflected ray, and the normal at the point of incidence lie in the same plane.
Law: Snell’s Law of Refraction
n1 sin i = n2 sin r
\[\frac{\sin i}{\sin r}=\frac{v_1}{v_2}\]
Law: Huygens' Principle
"Each point on a wavefront acts as a secondary source of light emitting secondary light waves called wavelets in all directions which travel with the speed of light in the medium. The new wavefront can be obtained by taking the envelope of these secondary wavelets travelling in the forward direction and is thus, the envelope of the secondary wavelets in forward direction. The wavelets travelling in the backward direction are in effective".
Key Points: Introduction of Wave Optics
Wave Optics (Physical Optics) treats light as a wave, explaining phenomena like interference, diffraction, and polarisation, which Ray Optics cannot explain.
- A wavefront is an imaginary surface where all points of a wave have the same phase (constant phase surface with maximum or minimum value).
- The direction of propagation of a wave is always perpendicular to the wavefront.
- Wavefront of a point source is a sphere; it propagates radially outward.
Types of Wavefronts:
Key Points: Nature of Light
- Light consists of energy-carrying photons guided by the rules of electromagnetic (EM) waves.
- Commonly observed phenomena of light are broadly classified into three categories: Ray optics, Wave optics, and Particle nature of light.
- Light thus exhibits a dual nature — it behaves both as a wave (wave optics) and as a particle (photon/particle nature), depending on the phenomenon observed.
Key Points: Variation of Amplitude & Intensity
| Parameter |
Spherical Wavefront |
Plane Wavefront |
Cylindrical Wavefront |
| Obtained by |
Point source at finite distance |
Point source at infinity / large distance |
Extended/linear source (slit) |
| Example |
Tip of candle flame |
Sunlight |
Tube light |
| Wave normal |
Along radius (diverging) |
Parallel to each other |
Along the radius |
| Amplitude (A) vs distance (r) |
A ∝ \[\frac {1}{r}\]
|
A = constant |
A ∝ \[\frac {1}{\sqrt r}\] |
| Intensity (I) vs distance (r) |
I ∝ \[\frac {1}{r^2}\] |
I = constant |
I ∝ \[\frac {1}{r}\] |
Key Points: Diffraction of Light
- Diffraction = bending and spreading of light waves around obstacles or through narrow openings, producing interference patterns.
- It is due to interference of secondary wavelets from the exposed portion of the wavefront from the slit.
- Key difference from interference: in diffraction, bright fringes have same intensity but bands are of decreasing intensity.
Single Slit Diffraction:
Let a = width of slit, θ = angle of diffraction.
Condition for Minimum (Dark) Intensity:
a sinθ = nλ, n = 1,2,3...
Condition for Maximum (Secondary Bright) Intensity:
\[a\sin\theta=(2n+1)\frac{\lambda}{2},\quad n=1,2,3...\]
Width of Central Maximum:
For first minima: \[a\cdot\frac{y}{D}=\lambda\Rightarrow y=\frac{\lambda D}{a}\]
\[W=2y=\frac{2\lambda D}{a}\]
Angular width of central maximum:
\[2\theta=\frac{2\lambda}{a}\]
Linear width of n-th secondary maximum:
\[\beta=\frac{\lambda D}{a}\]
Key Points: Total Internal Reflection
- Total internal reflection occurs when light travels from a denser medium to a rarer medium.
- It takes place only when the angle of incidence is greater than the critical angle.
- At angles greater than the critical angle, no refraction occurs.
- The entire light ray is reflected back into the denser medium.
- The intensity of the reflected ray becomes maximum and the phenomenon is used in optical fibres.
Key Points: Refraction of Light at a Plane Boundary Between Two Media
- Refraction at a plane boundary can be explained using Huygens’ principle and secondary wavelets.
- When light enters a denser medium, its speed decreases and the wavefronts become closer.
- The refracted image is not laterally inverted, but it appears bent (broken) at the boundary for oblique incidence.
- The wavelength of light changes when it enters a different medium; it decreases in a denser medium.
- The frequency remains unchanged while passing from one medium to another.
Key Points: Light Sources and Wavefronts
- Primary sources emit their own light (e.g., the Sun, stars, a bulb); secondary sources reflect or scatter light (e.g., the Moon, planets).
- A wavefront is the locus of all points having the same phase at a given instant of time.
- The direction of propagation of light is perpendicular to the wavefront (along the rays).
- A point source produces spherical wavefronts; far from the source, they appear as plane wavefronts.
- A line source produces cylindrical wavefronts; the wave speed equals the speed at which the wavefront moves.
Key Points: Resolving Power
- Resolution depends on diffraction effects caused by the optical instrument's aperture.
- According to Rayleigh’s criterion, two objects are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other.
- For a single slit (linear objects), the limit of resolution:
dθ = \[\frac {λ}{a}\]
- In a microscope, resolving power increases with numerical aperture (N.A. = n sin α) and decreases with wavelength:
R ∝ \[\frac {N.A.}{λ}\]
- For self-luminous point objects (microscope):
a = \[\frac {0.61λ}{N.A.}\]
- For a telescope, angular resolution is:
θ = \[\frac {1.22λ}{D}\]
where D is the aperture diameter.
- Resolving power improves when:
Wavelength is smaller
Aperture diameter is larger
The numerical aperture is higher
Key Points: Light as a Wave
- Light is a transverse electromagnetic wave consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation.
- Light does not require a medium and travels in a vacuum at the speed of light
c = 3 × 108 m/s
Refractive index n = \[\frac {c}{v}\]
- Visible light has wavelengths from 400–700 nm; different wavelengths produce different colours and cause dispersion (spectrum formation).
Key Points: Reflection of Light at a Plane Surface
- Reflection at a plane surface can be explained using Huygens’ principle and secondary wavelets.
- The reflected wavefront is formed as the envelope of secondary wavelets produced at the reflecting surface.
- The distance travelled by incident and reflected waves in the same time is equal (AE = BC = vT).
- The size of the image formed by a plane mirror is equal to the size of the object.
- The image formed in a plane mirror shows lateral reversal (right and left are interchanged).
Key Points: Interference
- Coherent sources emit waves of the same frequency with a constant phase difference.
- In Young’s double slit experiment, two coherent sources are obtained from a single source.
- Condition for constructive interference:
Path difference Δl = nλ
- Condition for destructive interference:
Path difference Δl = (n − \[\frac {1}{2}\])λ
- Position of bright fringe:
yn = \[\frac {nλD}{d}\]
- Fringe width:
W = \[\frac {λD}{d}\]
(Bright and dark fringes are equally spaced.)
- For a clear and steady interference pattern:
Sources must be coherent, monochromatic, of nearly equal amplitude, and slits must be narrow with D ≫ d.
key Points: Nature of Light
- Corpuscular theory (Newton): Light consists of particles called corpuscles that travel in straight lines; it explains reflection but fails to account for the correct speed in denser media.
- Wave theory (Huygens): Light behaves as a wave and accounts for reflection, refraction, interference, diffraction, and polarisation.
- Wave theory correctly states that the speed of light is lower in denser media, so light bends towards the normal.
- Geometrical (ray) optics studies light as straight-line rays; wave optics explains light using its wave nature.
- Dual nature of light: Light exhibits both particle nature (photons) and wave nature under different conditions.
