Osm Physics by Ashish

Motion Under Central Forces 1. Motion Under Central Forces (i) Central Force In any force field, if the force acting on a particle has the following characteristics: The line of action of the force passes through a fixed point called the centre of force . The magnitude of the force depends only upon the distance of the particle from the centre of force. Then the force is called a central force . Examples of central forces are the gravitational force and the electrostatic force . If the centre of force is taken at the origin, the central force can be written as \[ \vec{F}(\vec{r}) = F(r)\,\hat{r} \tag{1} \] where $\vec{r}$ is the position vector of the particle, $\hat{r}$ is the unit vector along $\vec{r}$, and $F(r)$ is the magnitude of the central force, which is a function of the distance $r$ from the centre o...

  Applications of Lasers A laser (Light Amplification by Stimulated Emission of Radiation) produces light that is highly coherent, monochromatic, directional, and intense . Due to these properties, lasers have a wide range of applications. 1. Industrial Applications Cutting and welding: High-power lasers are used for precise cutting and welding of metals and other materials. Drilling: Very small and accurate holes can be produced in hard materials. Marking: Lasers are used to mark serial numbers, barcodes, and designs on industrial products. Heat treatment: Laser beams can locally heat and modify the surface properties of materials. 2. Medical Applications Eye surgery: Lasers are used in procedures such as LASIK and retinal treatments. Surgery: Laser beams can cut or remove tissues with high precision and reduced bleeding. Dentistry: Lasers are used for treating dental cavities and soft-tissue procedures. Cancer treatment: Certain lasers are used in photod...

   Construction: It is a gas laser, which consists of a narrow quartz tube filled with a mixture of Helium and Neon gases in the ratio 10:1 respectively, at low pressure (~0.1 mm of Hg). Ne atoms act as active centers and responsible for the laser action, while He atoms are used to help in the excitation process. The length of the quartz tube is about 50 cm and the diameter is about 1 cm. Working: The common helium-neon gas laser achieves a population inversion in a different way. A mixture of about 10 parts of Helium and 1 part of Neon at a low pressure is placed in a glass tube that has parallel mirrors, one of them partly transparent, at both ends. The spacing of the mirrors is equal to an integral number of half-wavelengths of the Laser light. An electric discharge is produced in the gas by means of electrodes outside the tube connected to a source of high-frequency alternating current, and collisions with electrons from the discharge excite He and Ne atoms to metastable s...

  A ruby laser is a solid-state laser in which a ruby crystal acts as the active (lasing) medium. It was the first successfully demonstrated laser , developed by Theodore H. Maiman in 1960. The active medium is a ruby crystal , consisting of: A l 2 O 3 \mathrm{Al_2O_3} doped with a small amount of chromium ions ( C r 3 + ) (Cr^{3+}) , typically about 0.05% by weight . The C r 3 + Cr^{3+} ions are responsible for laser action. Construction A ruby laser consists mainly of: Ruby rod – acts as the active medium. Xenon flash lamp – provides optical pumping. Two reflecting mirrors – form the optical resonator. One mirror is fully reflecting . The other is partially reflecting and allows the laser beam to emerge. Power supply – provides high-voltage energy to the flash lamp. The ruby rod and flash lamp are generally placed inside an elliptical reflector so that maximum pump light is directed onto the ruby rod. Working Principle Ruby laser operates on the principle of stimulated em...

1.13 Mean Pressure of an Ideal Gas The average force exerted by the gas molecules per unit area of the wall is called the mean pressure or average pressure of the gas. Consider a rectangular container of volume \(V\) containing \(N\) molecules of an ideal gas, each of mass \(m\). Let the dimensions of the container be \(L_x\), \(L_y\), and \(L_z\). Therefore, \[ \boxed{V=L_xL_yL_z} \] Consider a molecule in the \(i\)-th state, having energy \(\varepsilon_i\), and moving in the \(X\)-direction. Let it exert a force \(F_i\) on the wall perpendicular to the \(X\)-axis. Suppose that the wall is displaced through a small distance \(dL_x\) by this force. If the system is isolated, the work done by ...

11. Motion of a System with Varying Mass: Rocket . Rocket A rocket employs the principle of jet propulsion . It may be a missile, spacecraft, or other vehicle that obtains thrust from a rocket engine. The exhaust of a rocket engine is produced entirely from propellants carried within the rocket before its launch. The operation of a rocket engine is based on Newton's third law of motion and the law of conservation of linear momentum . A rocket is propelled forward by ejecting exhaust gases backward at a very high velocity. A rocket engine consists essentially of propellant tanks, a combustion chamber, and a nozzle. The propellants may be gaseous, solid, liquid, or a combination of solid and liquid propellants. In the combustion chamber, a chemical reaction takes place between the fu...

Principle of LASER - Physics Notes Consider an atom having two energy levels \(E_m\) and \(E_n\), where \(E_n > E_m\). Let \(N_m\) and \(N_n\) be the number of atoms in the lower and upper energy levels, respectively. \[ E_n-E_m=h\nu \] The rate of absorption of radiation by atoms in the lower energy state is \[ R_{mn}=N_mP_{mn} \] \[ R_{mn}=N_mB_{mn}u(\nu) \] The total rate of emission from the upper energy state is the sum of spontaneous and stimulated emission: \[ R_{nm}=N_nP_{nm} \] \[ R_{nm}=N_n\left[A_{nm}+B_{nm}u(\nu)\right] \] Therefore, the ratio of total emission rate to absorption rate is \[ \frac{R_{nm}}{R_{mn}} = \frac{N_n}{N_m} \left[ 1+\frac{A_{nm}}{B_{nm}u(\nu)} \right] \tag{1} \] For non-degenerate energy levels, Einstein's relation gives \(B_{mn}=B_{nm}\). Therefore, \[ 1>>\frac{A_{nm}}{B_{nm}u(\nu)} \tag{1} \] Thus \[ \frac{R_{nm}}{R_{mn}}\approx\frac{N_n}{N_m}=e^{-h\nu/k_BT} \] Case-I if T=0 \...

Ratio of Spontaneous and Stimulated Transition Probabilities in Thermal Equilibrium The probability per unit time of spontaneous emission is P n m s p = A n m . P_{nm}^{\mathrm{sp}}=A_{nm}. The probability per unit time of stimulated emission is P n m s t = B n m u ( ν ) . P_{nm}^{\mathrm{st}}=B_{nm}u(\nu). Therefore, the ratio of spontaneous to stimulated emission probabilities is P n m s p P n m s t = A n m B n m u ( ν ) (1) \boxed{ \frac{P_{nm}^{\mathrm{sp}}}{P_{nm}^{\mathrm{st}}} = \frac{A_{nm}}{B_{nm}u(\nu)} } \tag{1} In thermal equilibrium, the spectral energy density of blackbody radiation is given by Planck's radiation law: u ( ν ) = A n m B n m 1 e h ν / k B T − 1 . u(\nu)= \frac{8\pi h\nu^3}{c^3} \frac{1}{e^{h\nu/k_BT}-1}. Using this expression in equation (1), where k B k_B  is Boltzmann's constant and T is the absolute temperature. Case I:  h ν ≫ k B T h\nu\gg k_BT When the photon energy is much greater than the thermal energy, e h ν / k B T ≫ 1. Therefore, P n m s...