Param Himalaya - परम हिमालय

Expression for de-Broglie wavelength :  According to quantum theory, the energy of a photon is given by $E = h\nu \qquad \dots (i)$ According to Einstein's mass-energy equivalence, the energy of the photon is $E = mc^2 \qquad \dots (ii)$ From equations (i) and (ii), we have, $mc^2 = h\nu$ $mc^2 = h\frac{c}{\lambda}( \because c = \nu \lambda)$ where, $\lambda$ is de-Broglie wavelength. $mc = \frac{h}{\lambda}$  $ \lambda = \frac{h}{mc} \qquad \dots (iii)$ But $mc = p$, the momentum of photon, therefore, $\lambda = \frac{h}{p} \qquad \dots (iv)$ If instead of a photon, we have a material particle of mass $m$ moving with velocity $v$, then eqn. (iii) becomes, $\lambda = \frac{h}{mv} \qquad \dots (v)$ which is the expression for de-Broglie wavelength. Conclusions. From eqn. (v), it is concluded that, (i) de-Broglie wavelength is inversely proportional to the velocity of the particle, i.e. $\lambda \propto \frac{1}{v}$. If particle moves faster, the wavelength of the wave associate...

Define Wave Nature of Matter ? Matter Waves or De-Broglie Waves The waves associated with moving material particles are known as De-Broglie waves or matter waves. According to a french physicist Louis de-Broglie, a moving material particle can be associated with a wave.In other words, a wave can guide the motion of a particle. Wave theory of electromagnetic radiation explains the phenomena of interference, diffraction and polarization. Whereas quantum theory of electromagnetic radiation successfully explains the photoelectric effect, Compton effect, black body radiation, X-ray spectra etc. This shows that, radiations have dual nature i.e. wave and quantum or particle nature. Louis de Broglie suggested that like radiations the particles like electrons, protons, neutrons etc have also dual nature. Dual nature i.e. the material particle can behave both as wave as well as particle.  His suggestion was based on the assumptions that : (i) the universe is made of particles and radiations....

What is a photon ( Particle Nature of Light )? Write the properties of a photon. When radiation interacts with matter, to cause emission of electrons, the radiation behaves as if it is made up of particles called photons. Thus, dual nature of radiation (i.e., wave and particle nature) was established. Photon is a packet of energy or quantum of energy ejected at the speed of light by an emitter. The energy of each bundle or packet or a photon is given by, $E = h\nu$ where $h$ is Planck's constant  $h= 6.63 \times 10^{-34} Js$ and $\nu$ is the frequency of radiation. Energy of $n$ photons is given by $E = nh\nu$ A source of radiation emits energy in packets when it goes from higher energy state to lower energy state and absorbs energy in packets when it goes from lower energy state to higher energy state. Properties of a Photon :  (i) A photon travels with a speed of light in vacuum (i.e. $3 \times 10^8 ms^{-1}$).} (ii) Rest mass of a photon is zero i.e. $m_0 = 0$. It means that...

Derive Einstein's Photoelectric Equation and Verify Laws of Photoelectric emission using this equation. According to Einstein, when a photon of energy $h\nu$ falls on a metal surface, the energy of the photon is used in two ways: (i) A part of photon energy is used by an electron to just cross over the surface barrier so that it may come out of the metal surface. This part of energy is equal to the work function ($\phi_0$) of the metal ; (ii) The remaining part of the photon energy is used in giving a velocity to the emitted photo electron. This part of energy is equal to the kinetic energy ($\frac{1}{2}mv^2$) of the emitted photo-electron. The process is shown in figure  According to the law of conservation of energy, $$h\nu = \phi_0 + \frac{1}{2}mv^2 \quad \dots (i)$$ If $\nu$ is just equal to threshold frequency $\nu_0$, then the free electron will just come out of the surface of metal and its kinetic energy is zero. i.e., $$h\nu_0 = \phi_0 + 0$$ $$h\nu_0 = \phi_0 \quad \dots (i...

Photoelectric effect cannot be explained on the basis of wave theory of light". Explain this statement. Photoelectric effect cannot be explained on the basis of wave theory of light because of the following reasons: [(i)] As per wave theory of light}, the electric field component ($E$) of light increases with the increase in the intensity of the light. When light falls on a metal surface, the force acting on a free electron in the metal surface increases with the increase in the intensity of the incident light ($F = -eE$). As a result of this, the kinetic energy acquired by the free electron increases with the increase in the intensity of the incident light. Contradiction : It is observed that the maximum kinetic energy acquired by photo electron ($\frac{1}{2}mv_{max}^2 = eV_0$) is same for both incident beams of different intensities $I_1$ and $I_2$ as shown in figure. This observation is contradictory to the fact explained with the help of the wave theory of light. [(ii)] As pe...

Describe an experiment to study photo-electric effect. The experimental set up to study photoelectric effect is shown in Figure :  It consists of a highly evacuated tube having two electrodes 'A' and 'C'. The electrode 'C' is a photo-sensitive emitter which emits photoelectrons when exposed to ultra-violet radiation. The electrode 'A' is a charge (or electrons) collecting plate. The tube has a side window made of quartz covered with a filter through which the incident light of desired wavelength enters the tube and falls on the photo-sensitive plate 'C'. Electrodes 'A' and 'C' are connected to a battery through a suitable reversing switch 'S'. Electrode 'A' can be brought to a positive or a negative potential with respect to electrode 'C' with the help of this switch. Procedure : Electrons are emitted when ultraviolet radiations are made to fall on photo-sensitive plate 'C'. These electrons get att...

Define and explain electron emission. Give different types of electron emissions. The phenomenon of emission of electron from a metal surface by supplying external energy is called electron emission. Explanation : In metals, the electrons in the outermost orbit of an atom are loosely bound and can move freely in all possible directions within the metal even at room temperature. These electrons in the metal are known as free electrons. These free electrons are responsible for the conductivity of a metal. However, these free electrons cannot leave the surface of the metal of their own. As soon as an electron tends to leave the metal surface, a positive charge is developed on the surface of the metal. This positive charge pulls back (or attracts) the free electron tending to leave the metal surface. This attracting force acts like a surface barrier for free electrons. The free electron can leave the metal surface only if an external energy is available to it to overcome the surface barrie...

State and explain Malus' law. The intensity of the plane polarised light transmitted through the analyser varies as the square of the cosine of the angle between the plane of transmission of the analyser and the plane of the polariser. Let $E$ be the amplitude of the light transmitted by the polariser and $\theta$ be the angle between the planes of the polariser and the analyser. Resolve $E$ into two components: (i) $E \cos \theta$ along $OP$ (i.e. parallel to the plane of transmission of analyser) (ii) $E \sin \theta$ along $OV$ (i.e. perpendicular to the plane of transmission of analyser). Only $E \cos \theta$ component is transmitted through the analyser. We know that, Intensity  $\propto (\text{Amplitude})^2$ i.e. $I \propto E^2$ Intensity of the transmitted light through the analyser is given by, $I \propto (E \cos \theta)^2 \quad \text{i.e.} \quad I = k E^2 \cos^2 \theta.$ But $k E^2 = I_0 \quad \text{i.e., the intensity of the incident polarised light}$ $I = I_0 \cos^2 \thet...

Notes : Class 12 Physics Chapter 2 Electrostatic Potential And Capacitance - Param Himalaya Chapter–2: Electrostatic Potential and Capacitance : Electrostatic potential energy  Electric potential   Potential difference Electric potential due to a point charge ELECTRIC POTENTIAL AT ANY POINT DUE TO AN ELECTRIC DIPOLE  ELECTRIC POTENTIAL DUE TO A GROUP OR SYSTEM OF POINT CHARGES (PRINCIPLE OF SUPERPOSITION OF POTENTIALS equipotential surfaces,  Electric Potential Energy of a System of Two and Three point charges   Expression for Potential Energy of Single and Two Charges in an External Electric Field    Electric Potential Energy of an Electric Dipole in an Electric Field  What do you understand by electrostatic shielding? Explain its significance . Behaviour of Conductors in the Electrostatic Field  capacitors and capacitance, Capacitance of a parallel plate capacitor . Effect of Dielectric on Capacitance. combination of capacitors in series ...

Viewing Single Slit Diffraction Pattern Diffraction pattern due to single slit can be easily seen by using an electric lamp with straight filament preferably and two razor (shaving) blades.  The shaving blades are held to form a narrow slit just near the eyes. Effort is made to see the filament through the slit. Bright and dark fringes are observed with slight adjustment of the width of slit. A single blade can also show diffraction of light. A slit made in aluminium foil can also be used for the purpose. Slit made by two fingers can also be used to observe diffraction of light.

The diffraction pattern due to a single slit obtained on a screen is shown in Angular width of a central maximum :   It is defined as the angle between the directions of the first minima on two sides of the central maximum. That is, angular width of central maximum is $2\theta$. The direction of the first minima on either side of the central maximum is given by $\theta = \frac{\lambda}{d} \quad \cdots (i) $ which is called half angular width of central maximum. Therefore, angular width of central maximum $= 2\theta = \frac{2\lambda}{d} \quad \cdots (ii)$ Linear width of central maximum :  Let $D$ be the distance of the screen from the centre $C$ of the slit. The linear distance of the first minima from the centre $O$ of the screen is given by $\because \text{ Arc } = \text{ angle } \times \text{ radius}$ $x = \theta D \quad $ $x = \frac{\lambda}{d} D = \frac{\lambda D}{d} \quad [\text{Using eqn. } (i)] $ The width of central maximum is equal to the linear distance between firs...

Describe diffraction of light at a single slit. Explain the formation of pattern of fringes on screen. Also, use the variation of intensity with diffraction angle $\theta$ to explain why the intensity of secondary maxima decreases with the order of maxima. Solution:  Let a diverging light from a monochromatic source S be made parallel after refraction through convex lens $L_1$. The refracted light forms a plane wavefront WW'. This plane wavefront WW' is incident on the slit AB of width $d$. According to Huygens' principle, each point of slit AB acts as a source of secondary disturbance or wavelets. Convex lens $L_2$ helps in converging the parallel beam of light. Now consider a point O equidistant from points A and B on the screen which is placed at a distance D from the slit AB. The secondary wavelets from A and B reach the point O in the same phase covering the same distance so constructive interference takes place at O. In other words, O is the position of central maximu...

Derive an expression for fringe width in Young's double slit experiment. State the factors on which fringe width depends.What is the shape of interference fringes obtained in Young's double slit experiment Dark and bright bands in the interference pattern are called interference fringes. Consider two coherent sources $S_1$ and $S_2$ separated by a distance $d$. Let $D$ be the distance between the screen and the plane of slits $S_1$ and $S_2$. Light waves emitted from $S_1$ and $S_2$ reach point O on the screen after travelling equal distances. So, path difference and hence phase difference between these waves is zero. Therefore, $S_1$ and $S_2$ meet at O in phase and hence constructive interference takes place at O. Thus, O is the position of the central bright fringe. Let the waves emitted by $S_1$ and $S_2$ meet at point P on the screen at a distance $y$ from the central bright fringe. The path difference between these waves at P is given by $ \Delta x = S_2P - S_1P \quad \cd...

Wavefronts Patterns for Mirrors , Lens and Prism - Param Himalaya (a) Wavefronts Patterns for Concave mirror :  A plane wavefront is reflected as a converging wavefront from a concave mirror. When a point source of light is at the focus of the concave mirror, then diverging spherical wavefronts fall on the concave mirror. (b) Wavefronts Patterns for Prism : A plane wavefront incident on a prism emerges out as a plane wavefront from the prism. (c) Wavefronts Patterns for Convex lens : A plane wavefront emerges out of a convex lens as a converging wavefront. Let a point source of light be at the focus of a convex lens such that diverging spherical wavefronts fall on the convex lens. The refracted wavefront will be a plane wavefront. (d) Wavefronts Patterns for Concave lens : a concave lens takes a plane wavefront and transforms it into a diverging spherical wavefront. (e) Wavefronts Patterns for Convex mirror : A convex mirror takes a plane wavefront and reflects it as a diverging ...

Huygens' Principle: Understanding Wave Propagation Huygens' Principle is a fundamental concept in optics that helps us understand how light and other waves propagate through a medium. It provides a geometrical way to determine the new position of a wavefront at any given instant, knowing its position at an earlier time. Statement of Huygens' Principle Huygens' Principle can be stated in three key postulates: Each Point on a Wavefront Acts as a Source: Every point on an existing wavefront serves as a source of secondary wavelets. These wavelets spread out in all directions with the speed of the wave in that medium. The initial wavefront is the locus of all points vibrating in the same phase. Secondary Wavelets Propagate: These newly generated secondary wavelets are spherical in shape (in a homogeneous medium) and travel outwards with the same velocity as the original wave. The New Wavefront is the Forward Envelope: The new position of the wavefront at...

Wavefront and Types of Wavefronts :  Define wavefront. Discuss various types of wavefronts namely spherical wavefronts, cylindrical wavefronts and plane wavefronts. Definition of Wavefront :  Wavefront is defined as the locus of all the particles of a medium vibrating in the same phase at a given instant. The shape of a wavefront depends upon the shape of the source of disturbance. Types of Wavefronts :  (a) Spherical wavefront (SWF):  If the source of disturbance is a point source (O), then the wavefront is spherical. A point source of light emits waves which spread outward in all directions. If the medium is homogeneous, then after time $t$ seconds, the wave or disturbance will travel a distance equal to $vt$(sphere radius), from the point source in all directions. In means, the particles of the medium lying on the surface of the sphere of radius $vt$ will get disturbed at the same moment i.e., all these particles will vibrate in the same phase. In this case, the s...

Notes : Class 12 Physics Chapter 10 Wave Optics - Param Himalaya  Wave front and It's types   Huygen’s principle refraction and Reflection of plane waves using Huygen’s principle.  Wavefronts Patterns for mirror, lens and prism Coherent and Incoherent Addition of Waves  Interference,  Young's double slit experiment and expression for fringe width coherent sources and sustained interference of light,  Diffraction due to a single slit Width of central maxima Malus' law.

Combination of Thin Lenses in Contact Equivalent Focal length, Power and Magnification  (i) Equivalent focal length of the combination of Lenses :  Consider two thin lenses of focal lengths $f_1$ and $f_2$ respectively, placed in contact with each other . Let $O$ be the point object placed on the principal axis of the lenses in contact. If the first lens forms an image $I_1$ of the object $O$ at a distance $v_1$ from it. $\frac{1}{v_1} - \frac{1}{u} = \frac{1}{f_1} \quad \text{(Lens formula)} \quad \dots (i)$ Since the second lens is in contact with the first, so $I_1$ acts as a virtual object for the second lens which forms the image $I$ at a distance $v$ from it. $\frac{1}{v} - \frac{1}{v_1} = \frac{1}{f_2} \quad \dots (ii)$ Adding eqs. (i) and (ii), we get $\frac{1}{v_1} - \frac{1}{u} +\frac{1}{v} - \frac{1}{v_1}$ $\frac{1}{v} - \frac{1}{u} = \frac{1}{f_1} + \frac{1}{f_2}$ or $\frac{1}{F} = $\frac{1}{v} - \frac{1}{u} \quad \dots (iii)$ Where $\frac{1}{F} = \frac{1}{f_1} + \...

Show that the bottom of a water tank appears to be raised. Hence find an expression for the normal shift in the position of an object placed in a denser medium. Consider a tank filled with water upto the level PQ. Let an object O (say a coin) lies at the bottom of the water tank. The depth AO = $t$ of the object is known as the real depth. the object appears at position I instead of O when viewed obliquely. The depth AI is known as apparent depth of the object O.  According to Snell's law, ${ }^{w}n_{a} = \frac{\sin i}{\sin r} \quad \dots (i)$ From $\Delta AOC$,  $\sin i = \frac{AC}{OC}$ and  from $\Delta AIC$,  $\sin r = \frac{AC}{IC}$ Substituting the values of $\sin i$ and $\sin r$ in equation (i), we get ${ }^{w}n_{a} = \frac{\frac{AC}{OC}}{\frac{AC}{IC}}$ ${ }^{w}n_{a} = \frac{AC}{OC} \times \frac{IC}{AC} = \frac{IC}{OC}$ Since point C lies very close to A, so IC $\approx$ AI and OC $\approx$ AO ${ }^{w}n_{a} = \frac{AI}{AO}$ ${ }^{a}n_{w} = \frac{1}{{ }^{w}n_{a...

Notes : Class 12 Physics Chapter 9 Ray Optics and Optical Instruments - Param Himalaya  Definition and Law of Reflection Sign convention for Reflection of light . Derive Relation Between Focal Length and Radius of Curvature Derive Mirror Formula ( Equation ) and Magnification for Convex mirror. Derive Mirror Formula and Magnification For Concave Mirror - Real and Virtual Image Refraction of light Principle of reversibility  Refraction of light through a Glass slab   Real depth and Apparent depth Total internal reflection , Optical Fibres   Refraction at a Spherical Surface Derivation - Lens Maker's Formula Refraction by a lens Power of Lens Combination of thin lenses in contact Refraction of light through a prism.  Simple Microscope and their magnifying powers Optical instruments: Compound Microscope and their magnifying powers . Astronomical telescopes and their magnifying powers.