Physics Vidyapith ✍️

Absorption → When a photon (or light) incident on atoms then atoms absorb the energy from the photon and jump from a lower energy state to a higher energy state. This transition is known as induced absorption or stimulated absorption or simply as absorption. The process is represented as $A+h\nu=A^{*}$ Where$A$ → Lower energy state atom$A^{*}$ → Excited or Higher energy state atom Absorption Transition If $N_{1}$ and $N_{2}$ is the population of energy $E_{1}$ and $E_{2}$, the number of atoms per unit volume that makes upward transitions from the lower levels to the upper level per second is called the rate of absorption transitions. It is represented by $R_{abs}=-\frac{dN_{1}}{dt} \qquad(1)$ Where $-\frac{dN_{1}}{dt}$ is rate of decrease of population at the lower energy level $E_{1}$ The rate of absorption transition can also be represented by the rate of the increase of population at the upper energy level $E_{2}$. i.e $R_{abs}=\frac{dN_{2}}{dt} \qquad(2)$

Derivation of Einstein Coefficient Relation→ Let us consider the $N_{1}$ and $N_{2}$ is the mean population of lower energy state and upper energy state respectively. If the energy density of incident light is $\rho(\nu)$ then The rate of transition of number of atoms due to absorption process: $R_{abs}=B_{12} \: \rho(v) \: N_{1} \qquad(1)$ The above equation shows the number of atoms absorbing the photon per second per unit volume Where $B_{12}$= Einstein Absorption Coefficent The rate of transition of number of atoms due to sponteneous emission process: $R_{sp}=A_{21} \: N_{2} \qquad(2)$ The above equation shows the number of atoms emitting the photon per second per unit volume due to spontaneous emission Where $A_{21}$= Einstein Spontaneous Emission Coefficient The rate of transition of the number of atoms due to stimulated emission process: $R_{st}=B_{21} \: \rho(v) \: N_{2} \qquad(3)$ The above equation shows the number of atoms emitting the photon per

Laser→ LASER is an acronym for  Light Amplification by Stimulated Emission of Radiation . It is a device that produces a highly intense monochromatic, collimated, and highly coherent light beam. Laser action mainly depends on the phenomenon of population inversion and stimulated emission. The first successful Laser is a solid-state laser which was built by TH Maiman in 1960 using Ruby as an active medium. Note→ The laser has often been referred to as an optical MASER because it operates in the visible spectrum portion of the spectrum. In general, when the variation occurs below the infrared portion of the electromagnetic spectrum, the term MASER will be employed, and when stimulated emission occurs in the infrared, visible, or ultraviolet portion of the spectrum the term laser or optical MASER will be used. Properties of a Laser Beam→ The laser beam has the following main characteristics properties: A laser beam has high directionality and can be em

The equation for missing order in the double-slit diffraction pattern→ The nature of the diffraction pattern due to the double slits depends upon the relative values of $e$ and $d$. If, however, $e$ is kept constant and $d$ is varied, then certain orders of interference maxima will be missing. We know that, the direction of interference maxima $(e+d)\:sin\theta=\pm n\lambda \qquad(1)$ The direction of diffraction minima $e \: sin\theta=\pm m\lambda \qquad(2)$ Divide the equation $(1)$ by equation $(2)$ $\frac{(e+d)}{e}=\frac{n}{m}$ Case (I)→ If $e=d$ then n=2m So for $m=1,2,3,....$ The $n=2,4,6,....$ Thus, the $2_{nd}, 4^{th}, 6^{th}, ...$ order interference maxima will be missing. Case (II) → If $e=\frac{d}{2}$ then n=3m So for $m=1,2,3,....$ The $n=3,6,9,....$ Thus, the $3_{rd}, 6^{th}, 9^{th}, ...$ order interference maxima will be missing.

A diffraction grating (or $N$-slits) consists of a large number of parallel slits of equal width and separated from each other by equal opaque spaces. It may be constructed by ruling a large number of parallel and equidistance lines on a plane glass plate with the help of a diamond point. the duplicates of the original grating are prepared by pouring a thin layer of colloidal solution over it and then allowed to Harden. This layer is then removed from the original grating and fixed between two glass plates which serve as a plane transmission grating. Generally, A plane transmission grating has 10000 to 15000 lines per inch. Diffraction due to N- slits OR Grating Theory→ Since plane diffraction grating is an $N$-slit arrangement, the deflection pattern due to it will be the combined diffraction effect of all such slits. Let a plane wavefront of monochromatic light be incident normally on the $N$-parallel slit of the gratings. Each point within the slits then sends out s

Let a plane wavefront be incident normally on slit $S_{1}$ and $S_{2}$ of equal $e$ and separated by an opaque distance $d$.The diffracted light is focused on the screen $XY$. The diffracted pattern on the screen consists of equally spaced bright and dark fringe due to interference of light from both the slits and modulated by diffraction pattern from individual slits. op The diffraction pattern due to double-slit can be explained considering the following points → All the points in slits $S_{1}$ and $S_{2}$ will send secondary waves in all directions. All the secondary waves moving along the incident wave will be focussed at $P$ and the diffracted waves will be focussed at $P'$ The amplitude at $P'$ is the resultant from two slit each of amplitude $R=\frac{A\:sin\alpha}{\alpha}$ T two waves from two-slit $S_{1}$ and $S_{2}$ will interfere at $P'$ Fraunhofer diffraction due to double slits Expression for Intensity → $\Delta = S_{2}M$

Dispersive power of plane diffraction grating: The dispersive power of a diffraction grating is defined as: The rate of change of the angle of diffraction with the change in the wavelength of light are called dispersive power of plane grating. If the wavelenght changes from $\lambda$ to $\lambda +d\lambda$ and respective change in the angle of diffraction be from $\theta$ to $\theta+d\theta$ then the ratio $\left(\frac{d\theta}{d\lambda} \right)$ Expression of Dispersive power of a plane diffraction grating: The grating equation for a plane transmission grating for normal incidence is given by $(e+d)sin\theta=n\lambda \qquad(1)$ Where$(e+d)$ - Grating Element$\qquad \:\: \theta$ - Diffraction angle for spectrum of $n^{th}$ order Differentiating equation $(1)$ with respect to $\lambda$, we have $(e+d)cos\theta \left( \frac{d\theta}{d\lambda} \right)=n$ $\frac{d\theta}{d\lambda}=\frac{n}{(e+d)cos\theta}$ $\frac{d\theta}{d\lambda}=\frac{n}{(e+d)\sqrt{

Let $S$ be a point monochromatic source of light of wavelength $\lambda$ placed at the focus of collimating lens $L_{1}$. The light beam is incident normally from $S$ on a narrow slit $AB$ of width $e$ and is diffracted from it. The diffracted beam is focused at the screen $XY$ by another converging lens $L_{2}$. The diffraction pattern having a central bright band followed by an alternative dark and bright band of decreasing intensity on both sides is obtained. Analytical Explanation: The light from the source $S$ is incident as a plane wavefront on the slit $AB$. According to Huygens's wave theory, every point in $AB$ sends out secondary waves in all directions. The undeviated ray from $AB$ is focused at $C$ on the screen by the lens $L_{2}$ while the rays diffracted through an angle $\theta$ are focussed at point $p$ on the screen. The rays from the ends $A$ and $B$ reach $C$ in the same phase and hence the intensity is maximum. Fraunhofer diffraction due to

Interference of light: When two or more waves, having the same frequency and constant phase difference, travel simultaneously in the same region of a medium, these waves superimpose on each other and a resultant wave is obtained which has intensity at some points maximum and some points minimum in the region. This is phenomenon is known as interference of light. When the intensity of the resultant wave is maximum in the region then this is called constructive interference. when the intensity of the resultant wave is minimum in the region then this is called destructive interference. Classification of Interference: The phenomenon of interference may be grouped into two categories depending upon the formation of two coherent sources in practice.The interference of light is classified into two categories: Division of amplitude Division of wavefront Division of amplitude: In this method, the amplitude of the incident beam is divided into two or mo

Newton's Rings: Experimental Arrangement: A plano-convex lens $l_{1}$ of large radius of curvature is placed on a plane glass plate $G_{1}$ with the curved surface touching the glass plate. An air film is enclosed between the curved surface of the lens and the glass plate. A sodium vapor lamp $S$ is kept at the focus of a biconvex lens $L$ which converts the diverging beam of light into a parallel beam. The parallel beam of light is made to fall on a glass plate $G_{2}$ kept at an angle of $45^{\circ}$ with the incident beam. A part of incident light is reflected toward the plano-convex lens. This light is again reflected back, partially from the top and partially from the bottom of the air fil and transmitted by the glass plate $G_{2}$. The interference of these rays is observed through a microscope $M$. Newtons Rings Experiment Setup-Ray Diagram Explanation of the formation of Newton's rings: Division of amplitude takes

Derivation of Fringe width of the wedge-shaped thin film: The distance between two consecutive bright (or dark) fringes is called the fringe width. If the $n^{th}$ bright fringe is formed at a distance $x_{n}$ from the edge of the wedge shaped film where the thickness is $t_{n}$. So the path difference for $x_{n}$ bright fringe: $(2n-1) \frac{\lambda}{2}= 2 \mu \: t_{n} \: cos(\alpha+r) \qquad(1)$ For Normal IncidenceThe incident Angle $i=0$The refracted Angle $r=0$ then from equation $(1)$ $(2n-1) \frac{\lambda}{2}= 2 \mu \: t_{n} \: cos\alpha \qquad(2)$ Fringe width of wedge-shaped thin film for normal incidence From the figure, In $\Delta OAB$ $tan \alpha = \frac{t_{n}}{x_{n}}$ $t_{n}=x_{n} \: tan \alpha \qquad(3) $ Now put the value of $t_{n}$ in equation $(2)$ $(2n-1) \frac{\lambda}{2}= 2 \mu \: x_{n} \: tan \alpha \: cos\alpha $ $(2n-1) \frac{\lambda}{2}= 2 \mu \: x_{n}\: \frac{sin \alpha}{cos\alpha} \: cos\alpha $ $(2n-1) \frac{\lam

Derivation of interference of light due to a wedge-shaped thin film: Interference of light due to wedge-shaped thin film The wedge-shaped film is bound by two plane surfaces inclined at angle $\alpha$. The thickness t of the film varies uniformly from zero at the edge to its maximum value at the other end. A Ray of light ab incident on the film will be partially reflected along be and partially transmitted along $BC$. The ray $BC$ will be partially reflected along $CD$ which will be again partially transmitted along $BF$. The two rays $BE$ and $DF$ in reflected light diverge. The path difference between ray $BE$ and $DF$ is $\Delta=\mu(BC+CD)-BG \qquad(1)$ Where $\mu$- Refractive index of the film $\Delta CDJ$ and $\Delta CHJ$ are congruent so $ \begin{Bmatrix} CD=CH \\ DJ=JH=t \end{Bmatrix} \qquad(2)$ From equation $(1)$ $\Delta=\mu(BK+KC+CH)-BG \qquad (\because BD=BK+KC)$ $\Delta=\mu(BK+KH)-BG \qquad (3)$ In $\Delta BDG$- $sin\:i = \f

Derivation of interference of light due to thin-film: Let's consider a Ray of light $AB$ incident on a thin film of thickness $t$ and the refractive index of a thin film is $\mu$ The ray $AB$ is partially reflected and partially transmitted at $B$. The transmitted BC is against partially transmitted and partially reflected at $C$. The reflected ray $CD$ is partially reflected and partially refracted at $D$. Propagation of light ray in thin film The interference pattern in reflected light will be due to ray $BF$ and $DH$ which are coherent as they are both derived from the same Ray $AB$. The interference pattern in transmitted light will be due to ray $CI$ and $EJ$. The path difference between $BF$ and $DH$ ray will be $\Delta=\mu(BC+CD)-BG \qquad(1)$ The triangle $\Delta BCK$ and $\Delta CDK$ are congruent because $\begin{Bmatrix} BK=KD \\ BC=CD \\ CK=t \end{Bmatrix} \qquad (2)$ From equation $(1)$ and $(2)$ $\Delta=2 \mu BC-BG \qquad(3)$ I