Welcome to my website! I'm Vivek Chandra, and here I showcase projects related to optics and atomic physics that I've explored during my bachelors and masters in the physics laboratory. My focus is on delving into the principles and theories behind these projects, highlighting the results we can obtained, and discussing the valuable insights that we can learn from them.
Hydrogen emission spectra (To Determine the Rydberg's Constant)
Explanation of Apparatus Used :
(a)Grating
Grating Formula used :
where, e= slit width
d= distance between slits
θ = diffraction angle
When I look through the grating in the presence of white light emitted by a lamp, it reveals a spectrum of colors. Since the white light from the lamp contains all colors, the grating separates these colors, creating a beautiful and vivid display.
(b) Spectrometer
1.Slit: Narrow opening controlling the amount of light entering the spectrometer.
2.Collimator:The collimator is a lens system that takes the diverging light from the entrance slit and produces parallel rays.
3.Prism Table: Platform for holding and adjusting prisms or grating that disperse light.
4.Eyepiece: Optical element for viewing the spectrum
5.Telescope: Collects and focuses dispersed light.
Theory & Methodology :
The Rydberg constant is measured by studying the hydrogen emission spectrum in the visible region using a diffraction grating & spectrometer. we choose the balmer series because its transistion wavelength comes in visible spectra.
(a) Hydrogen Discharge Tube
(b) Experimental setup
The hydrogen discharge tube involves a sealed glass tube containing hydrogen gas at low pressure. When an electric current is applied, the hydrogen atoms become energized, emitting light in the form of discrete spectral lines. This emitted light passes through a grating which disperses the light into its different components based on wavelength. The result is a spectrum of colors on a screen or detector, each line corresponding to a specific electron transition in the hydrogen atoms.
(c) Emission
Here, for Hα (nf=2 and ni=3) (see as redline in spectrum)
we first find λ using grating formula by determining the angle of diffraction using spectrometer and then find RH,
similarly for, Hβ (nf=2 and ni=4), see as blue-green line in spectrum
& Hγ (nf=2 and ni=5), see as Blue line in spectrum
we again find RH and then take the average of these three values of RH.
hence, RH = Rydberg's constant can be found.
2. Sodium emission spectra (To determine wavelength of D1 and D2 line)
Theory & Methodology:
(a)Splitting due to spin-orbit coupling
The D1 and D2 lines in the sodium spectrum refer to specific wavelengths of light emitted by excited sodium atoms during electron transitions. These lines are part of the fine structure of the sodium spectrum. The fine structure is a consequence of spin-orbit coupling, which causes the energy levels to split into sub-levels. As electrons transition between these sub-levels, they emit light at specific wavelengths, giving rise to the fine structure observed in the sodium D lines. The D lines, is at approximately 589.0 nm (D1) and 589.6 nm (D2).
(a)For 3p
L=1 & S=1/2 , so J=1/2 and 3/2, hence 3p level splits into two sublevels.
(b)For 3s
L=0 & S=1/2 so J=1/2 , hence it has only one level so it does not split
further.
(b) Schematic of experimental setup
Light source coming from sodium lamp passes via collimator of spectrometer then its disperse in various components after passsing through prism, by using the formula of grating we can obtain the value of wavelength for D1 and D2 line.
(c)Experimental setup
Conclusion:
The experimental determination of the wavelengths for the D1 and D2 lines in the sodium spectrum yielded values of approximately 589.0 nm for D1 and 589.6 nm for D2. Consequently, considering the minimal separation between D1 and D2, we can effectively considered the sodium lamp as a nearly monochromatic source of light.
3. Faraday Rotation (To determine verdet's constant)
Theory & Methodolgy:
Faraday rotation is a phenomenon where the plane of polarization of linearly polarized light rotates as it passes through a magnetic field. This effect is named after Michael Faraday, who first observed it in 1845.It can be understood as the result of incident plane-polarized light being a combination or superposition of right circularly polarized light (RCPL) and left circularly polarized light (LCPL) .When this light passes through a medium with magnetic properties, the magnetic field induces a circular motion of electrons in the material. This circular motion affects the propagation speed of RCPL and LCPL differently. As a result, when the RCPL and LCPL components recombine after passing through the magnetic field, the resulting linearly polarized light is rotated by an angle known as the Faraday rotation angle (θ). This rotation angle is directly proportional to the strength of the magnetic field (B) and the length of the solenoid(L) used in the setup.
Fig: Rotation of PPL
here, θ = BvL
where, θ= Angle rotated after magnetic field is on
v= verdent constant (different for different material)
L=length of solenoid
Experimental setup use :
The sample material is placed inside the solenoid. We can calculate the rotation angle (θ ) and we know the length of the solenoid (L). Additionally, we are aware of the magnetic field (B) applied, determined using a gauss meter. Therefore, we can calculate the Verdant constant(v) using the following formula :
v = θ/BL
4. Fabry perot interferometer (To determine spacing between etalon)
Theory :
The Fabry Perot Interferometer is a device which utilizes the interference due to division of amplitude to provide high resolution circular fringes. It is often employed to do spectral analysis of a visible light source.
To get an interference pattern, a coherent source of visible light is allowed to fall on a parallel set of partially silvered mirrors called an etalon which then interfere after multiple reflections and transmissions to produce a set of circular fringes which are fringes of equal inclination.
Experimental setup :
We consider a set of 2 partially silvered mirrors placed parallel to each other in air. The amplitude reflection coefficient is and the amplitude transmission coefficient is .
We let a monochromatic source of light fall on the mirror at an angle with the normal to the mirrors.
Intensity Distribution :
ETALON SPACING CALCULATION :
RESULTS :
(a) Using Red laser
(b) Using Green Laser
5. Electron spin resonance (To determine Spin lande g-factor)
Theory & Approach :
Our primary goal is to explore and determine the Landé g_s factor, a crucial parameter associated with the electron's spin behavior. To conduct this experiment, we utilize a sample of 2,2-diphenyl-1-picrylhydrazyl (DPPH), a paramagnetic material featuring unpaired electrons.
When a paramagnetic material is subjected to a magnetic field, electrons with associated magnetic moments start precessing or revolving around the magnetic field axis, forming an angle with a characteristic frequency called the Larmor frequency. By supplying external energy in the form of microwave radiation(Rf field) with a frequency matching the Larmor frequency, a resonance condition is achieved. This resonant absorption causes the transition of electrons from the lower energy state (E1) to a higher energy state (E2). The change in energy configuration is detected on the oscilloscope, where a distinct peak corresponds to the resonance condition. The study of these resonance phenomena allows us to determine the Landé g_s factor.
Experimental setup :
(a)Block diagram of experimental setup
(b) Experimental setup and output
here, the helmholtz coil is used to provide the constant magnetic field at the center where our sample DPPH is present.The peaks in the output of oscilloscope is corresponding the resonance.We get more than one peak because our Rf field is a sinusoidal curve so this larmor frequency comes again and again.
6. Franck hertz experiment
Theory :
The Franck-Hertz experiment, conducted by James Franck and Gustav Hertz in 1914, provided crucial evidence for the quantization of energy levels in atoms, supporting the emerging quantum theory. In the experiment, electrons are accelerated through a gas, typically Argon, and allowed to collide with Argon atoms. As the electron energy increases, it collides with the Argon atoms and transfers energy to them. The most significant observation is a distinct pattern in the current-voltage curve, revealing that electrons must possess discrete amounts of energy to excite the Argon atoms. When the electron energy matches the energy difference between the ground state and an excited state of the Argon atom, decrease in current occurs. This quantized behavior confirmed the concept of quantized energy levels in atoms, a fundamental tenet of quantum mechanics.
Experimental Setup & Approach :
Fig: Experimental setup
The electrons emitted by filament can be accelerated by the potential VG2K between the cathode and the grid G2. The grid G1 helps in minimizing space charge effects. The grids are wire mesh and allow the electrons to pass through. The plate (A) is maintained at a potential slightly negative with respect to the grid G2. This helps in making the dips in the plate current more prominent. In this experiment, the electron current is measured as a function of the voltage VG2K. As Voltage increases, the electron energy goes up and so the electron can overcome the retarding potential VG2A to reach the plate (A). This gives rise to a current in the ammeter, which initially increases. As the voltage further increases, the electron energy reaches the threshold value to excite the atom in its first allowed excited state. In doing so, the electrons lose energy and therefore the number of decreases. This decrease is proportional to the number of inelastic collisions that have occurred. When the VG2K is increased further and reaches a value twice that of the first excitation potential, it is possible for an electron to excite an atom halfway between the grids, loose all its energy, and then gain a new enough energy to excite another atoms resulting in a second dip in the current.
Result :
7. Newton Ring's (To determine wavelength of incident light)
Theory & Approach :
The Newton's rings experiment involves placing a plano-convex lens on a flat glass surface. When illuminated with monochromatic light, a series of concentric, alternating bright and dark rings, known as Newton's rings, are observed. These rings result from the interference between the reflected light rays R1 & R2 or transmitted rays T1 & T2.
Path difference between R1 & R2 is ------------------------------------------------------>
Consider a ring of radius r due to thickness t of air film
Condition for bright ring
Finding wavelength
Output
Experimental setup:
8. Brewster angle (To determine refractive index of material)
Theory :
At Brewster's angle, the reflected light is completely polarized perpendicular to the plane of incidence (S-polarization), while the transmitted light is partially polarized parallel to the plane of incidence. The relationship is described by the tangent of the Brewster angle, which equals the ratio of the refractive indices.
Experimental setup & Approach :
The process begins by sending unpolarized monochromatic light from a sodium lamp. The light strikes a surface at an angle, and by adjusting the telescope of a spectrometer, we identify the angle at which rotating a polarizer causes the light's intensity to vanish completely. This specific angle is termed the Brewster angle. Utilizing the Brewster angle, we can determine the refractive index (n) of material using the formula
n=tan(θ) ,where θ=Brewster angle
particularly when the incident medium is air. (so n1=1)
9.Wedge shaped film (To determine thickness of thin paper)
Theory & Approach :
Wedge-shaped film involves the study of interference fringes produced by light passing through a thin wedge of transparent material. This phenomenon is explained through the division of amplitude approach. When monochromatic light is incident on the wedge, it undergoes both reflection and transmission at the two surfaces of the wedge. These two waves (C&E) interfere with each other, creating a pattern of fringes.
Condition for maxima & calculating thickness of thin paper
Experimental setup
(a) Experimental setup
(b) Interference Fringes
Its experimental setup is similar to as in newton's ring instead of lens we use the arrangement of wedge film which can be formed by taking two slabs and attached by tape at one of the end and putting thin paper between two slabs in the second end which creates a wedge shaped or creating an inclination.
10. Fresnel Biprism (To determine the wavelength of incident light)
Theory & Approach:
Biprism is formed by merging two narrow prisms at their base. A narrow slit is placed before biprism so that slit is in line with centre of biprism.A single wavefront emerging from the narrow slit is getting refracted.After refraction, light rays merge together on a screen to form interference pattern. Refracted light rays are acting in this process such that as if they are coming from two virtual point sources of light.
(a)Calculation of D:
D=a+b
(b)Calculation of d:
To determine distance d between virtual sources we use images formed by convex lens as shown below
using magnification formula for lens :-
Experimental setup :
Result
(a) Experimental setup
(b) Interference frindges
