Chromatic dispersion is phenomenon in which the index of refraction depends on wavelength/frequency, so the speed of light through a material varies slightly with the frequency of the light and each λ is refracted at a slightly different angle. The longer λ, the smaller index of refraction n red
< n blue
, red light is refracted less than blue light
Electromagnetic waves are produced by the accelerated electric charges.
1. radio waves: antenna: an alternating current produces a radio wave
2. light : When an electron changes from a high energy level to a low one it emits electromagnetic radiation/photon. Energy of the photon equals the electron’s change in energy ΔE. The frequency of the emitted light, f is given by: ΔE = hf, where h is Planck’s constant 6.63 x 10
-34
Js
3. Even higher frequencies Electron energy levels are in the order of 10 eV. Much higher frequencies would need an energy change in the order of
MeV, much greater than electron energies. Radiation with such high energy comes from the nucleus.
• EM wave is a transverse wave, the electric and magnetic fields oscillate perpendicular to each other and also perpendicular to the direction of wave propagation, traveling through vacuum with the SAME SPEED! c ≈ 3 x 10
8
m/s, which is independent of the motion of the source . c = λf
• EM waves carry energy (as any wave does) which is directly proportional to its frequency, inversely proportional to its wavelength. In addition, energy/ intensity of a wave is proportional to its amplitude
2
.
When EM waves is incident upon some medium it will be transmitted, absorbed or scattered to different extend depending on both wavelength and medium involved.
If the Earth had no atmosphere , we would see the Sun as white star in sea of blackness.
Scattering is the process of absorption and reemission of a light wave in different direction.
A day-time sky is blue because molecules in the air (the nitrogen and oxygen molecules...) scatter blue light from the sun more than they scatter red light. Blue light is scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you.
At sunset sky is red . The path of the light through the atmosphere is longer, so there is more chance for the blue light to scatter multiple times, less chance to reach eye. When we look towards the sun at sunset, we see red and orange colours because the blue light has been scattered out and away from the line of sight.
A monochromatic source of radiation is one that has a extremely narrow band of frequencies.
Two sources are coherent if they ▪ have the same frequency ▪ maintain a constant phase difference with each other.
Two coherent waves have a phase difference which remains constant over time.
When a light bulb emits photons, they are emitted randomly in different directions and with different phase because the filament atoms act independently from each other. The light emitted is incoherent.
Laser light is a coherent and monochromatic source of electromagnetic radiation.
MASER Microwave amplification by stimulated emission of radiation LASER Light amplification by stimulated emission of radiation
Both apply the same principles (stimulated emission, existence of metastable state and population inversion) and only differ in the frequency range.
Spontaneous Emission: An atom in excited state returns to the lower state spontaneously. LED, lamp…
Stimulated Emission: Suppose an electron is already in an excited state and a photon comes along with energy equal to the difference in the energy between the excited state and the ground state of the atom or molecule.
P hoton will stimulate the electron to fall into the lower energy state emitting a photon which is in phase and in the same direction as original photon. This is resonance process, called stimulated emission.
One photon interacting with an excited atom results in two photons coherent photons (identical and in phase).
Population inversion: When a sizable population of electrons resides in higher energy level, this condition is called a "population inversion". I t is necessary to create a population inversion for laser action to occur.
Some atoms will undergo spontaneous emission, and the resulting photons cause other atoms to undergo stimulated emission, leading to a chain reaction. The resultant light is composed of one frequency, very intense, and coherent.
To have inverse population it is important that higher energy level is metastable state – excited state with longer lifetime, so the electrons can remain in this state for a longer period before they decay to the ground state.
constructive interference
– bright fringe
● intensity distribution of the fringes on the screen when the separation of the slits is large compared to their width.
The fringes are of equal intensity and of equal separation.
If the slit separation is decreased, the pattern will spread out. d sin

= (n + ½ ) λ destructive interference
– dark fringe

Multiple slits – diffraction grating
• bright fringes maintain the same separation. • bright fringes become much sharper.
• the overall amount of light being let through is increased, so the pattern increases in intensity.
If white light is viewed through a diffraction grating , each wavelength undergoes constructive interference at different angles. This results in a spectrum.
The individual wavelengths can be calculated from the angle using the formula d sin θ = n λ greater λ greater angle
Lenses : • Optical axis – axis of symmetry of a lens • Focal point – the point to which light rays parallel to the optical axis converge after passing through a converging lens. It is a real image of an object at infinite distance from lens. Because light can go both ways lens has two focal points.
Standard rays • ray parallel to optical axis is refracted through the lens through focal point F • ray coming through the centre of the lens will continue n the same direction • ray passing through F in front of the lens is refracted parallel to the axis image can be real/virtual, enlarged/diminished and in the same direction/inverted.
Real image is formed when the light passes through the actual image location. Such image can be caught on the screen.
Virtual image is image which is formed at the position where extended rays cross. For the eyes (and brain) it seems as if these refracted rays were coming from virtual image – intersection of the extended rays.
The Thin-Lens Equation
Linear magnification m = focal length f is + for a converging lens u is distance between lens and object: v is distance between lens and image: real object, image: positive u, v virtual object, image: negative u, v object, image upward: positive h o
, h i object, image downward: negative h o
, h i
Power of a lens (P) – measure of the extent of refraction of light: P (diopters) =
Optics of the eye:
Near Point = distance of the closest object that can be focused on the retina: D ≈ 25 cm
Far point = distance of the farthest object that can be focused on the retina = ~ infinity
Angular magnification of a simple microscope (magnifying glass) f greater – less curvature – less refraction – smaller P f smaller – more curvature – more refraction – greater P
M = telescope magnification unaided eye : the greatest possible apparent size will be if the object is at near point . If the object is closer, the image is not clear, if it is farther apparent size is smaller. for virtual image formed by lens at eye’s near point, angular magnification is:
M = + 1
If the object is placed at focal point of the lens, virtual image is formed at infinity. Eye is relaxed. angular magnification is:
M =

A compound microscope consists of two lenses — the objective lens and the eyepiece lens.
The first lens (the objective lens) forms a real magnified image of the object being viewed.
This real image can then be considered as the object for the second lens (the eyepiece lens) which acts as a magnifying glass.
The rays from this real image travel into the eyepiece lens and they form a virtual magnified image. In normal adjustment , this virtual image is arranged to be located at the near point so that maximum angular magnification is obtained.
M = m
1
m
2 angular magnification = linear magnification produced by eye piece x linear magnification produced by objective
An astronomical telescope also consists of two lenses. In this case, the objective lens forms a real but diminished image of the distant object being viewed (no other choice). Once again, this real image can then be considered as the object for the eyepiece lens acting as a magnifying lens. The rays from this real image travel into the eyepiece lens and they form a virtual magnified image. In normal adjustment , this virtual image is arranged to be located at infinity.
Angular magnification M =
The length of the telescope ≈ f o
+ f e
Difference between microscope and telescope: microscope: object is between F & 2 F of the objective first image is real, enlarged within focal length of the eyepiece, so the image formed by eyepiece is virtual and enlarged.
The situation with telescope is similar except that the object is at infinite distance and image formed by the first lens is real and smaller.
In an ideal lens, all light rays from one point of the object would meet at the same point of the image, forming a clear image. The influences which cause different rays to converge to different points are called aberrations.

Lenses do not form perfect images, and there is always some degree of distortion or aberration introduced by the lens which causes the image to be an imperfect replica of the object. Careful design of the lens system for a particular application ensures that the aberration is minimized. There are several different types of aberration which can affect image quality. (Wikipedia)
Spherical Aberration occurs because spherical surfaces are not the ideal shape with which to make a lens, but they are by far the simplest shape to which glass can be ground and polished (the least expensive) and so are often used. perfect lens spherical lens paralel light rays striking the outer edges of a lens are focused in a slightly different place than beams close to the axis.
This problem is not limited to parallel light. Any incident ray which strikes the outer edges of the lens is subject to this departure from the expected or proper course for the ideal lens . This manifests itself as a blurring of the image. Lenses in which closer-to-ideal, non-spherical surfaces are used are called aspheric lenses .
Correction for spherical aberration
this or money remember that all rays incident on the lens from the object will be focused, and that the image will be formed even if part of the lens is covered. The image will be simply dimmer.
A lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short wavelengths) is larger than that of red light (long wavelengths). The amount of chromatic aberration depends on the dispersion of the glass .
One way to minimize this aberration is to use glasses of different dispersion in a doublet or other combination
This effect can be reduced by having a combination of a convex and a concave lens made of glasses having different refractive indices.
Chromatic aberration can be minimized using additional lenses
In an Achromat, the second lens cancels the dispersion of the first.
Achromats use two different materials, and one has a negative focal length.