Param Himalaya - परम हिमालय

Lyrics : माँ शारदे कहाँ तू, वीणा बजा रही हैं ,Maa Sharde Kaha Tu Veena Baja Rahi Hai - सरस्वती वंदना  माँ शारदे कहाँ तू, वीणा बजा रही हैं, किस मंजु ज्ञान से तू, जग को लुभा रही हैं ॥ किस भाव में भवानी, तू मग्न हो रही है, विनती नहीं हमारी, क्यों माँ तू सुन रही है । हम दीन बाल कब से, विनती सुना रहें हैं, चरणों में तेरे माता, हम सर झुका रहे हैं । ॥ मां शारदे कहाँ तू, वीणा...॥ अज्ञान तुम हमारा, माँ शीघ्र दूर कर दो, द्रुत ज्ञान शुभ्र हम में, माँ शारदे तू भर दे । बालक सभी जगत के, सूत मात हैं तुम्हारे, प्राणों से प्रिय है हम, तेरे पुत्र सब दुलारे, तेरे पुत्र सब दुलारे । ॥ मां शारदे कहाँ तू, वीणा...॥ हमको दयामयी तू, ले गोद में पढ़ाओ, अमृत जगत का हमको, माँ ज्ञान का पिलाओ । मातेश्वरी तू सुन ले, सुंदर विनय हमारी, करके दया तू हर ले, बाधा जगत की सारी । ॥ मां शारदे कहाँ तू, वीणा...॥

Lyrics : हे शारदे माँ, ,Hey Sharde Maa प्रार्थना सरस्वती वंदना  हे शारदे माँ, हे शारदे माँ हे शारदे माँ, हे शारदे माँ अज्ञानता से हमें तार दे माँ हे शारदे माँ॥ तू स्वर की देवी, ये संगीत तुझसे हर शब्द तेरा है, हर गीत तुझसे हम है अकेले, हम है अधूरे तेरी शरण हम, हमें प्यार दे माँ हे शारदे माँ, हे शारदे माँ अज्ञानता से हमें तार दे माँ॥ मुनियों ने समझी, गुणियों ने जानी वेदों की भाषा, पुराणों की बानी हम भी तो समझे, हम भी तो जाने विद्या का हमको अधिकार दे माँ हे शारदे माँ, हे शारदे माँ अज्ञानता से हमें तार दे माँ॥ तू श्वेतवर्णी, कमल पर विराजे हाथों में वीणा, मुकुट सर पे साजे मन से हमारे मिटाके अँधेरे हमको उजालों का संसार दे माँ हे शारदे माँ, हे शारदे माँ अज्ञानता से हमें तार दे माँ॥ शारदे माँ, हे शारदे माँ अज्ञानता से हमें तार दे माँ हे शारदे माँ, हे शारदे माँ हे शारदे माँ, हे शारदे माँ॥

Lyrics : हे प्रभु आनंद-दाता, ज्ञान हमको दीजिए , Hey prabhu anand data gyan humko dijiye  हे प्रभु आनंद-दाता, ज्ञान हमको दीजिए, शीघ्र सारे दुर्गुणों को, दूर हमसे कीजिए। लीजिए हमको शरण में, हम सदाचारी बनें, ब्रह्मचारी धर्म-रक्षक, वीर व्रत धारी बनें। ॥ हे प्रभु आनंद-दाता ज्ञान हमको दीजिए...॥ निंदा किसी की हम किसी से, भूल कर भी न करें, ईर्ष्या कभी भी हम किसी से, भूल कर भी न करें। सत्य बोलें, झूठ त्यागें, मेल आपस में करें, दिव्य जीवन हो हमारा, यश तेरा गाया करें। ॥ हे प्रभु आनंद-दाता ज्ञान हमको दीजिए...॥ जाए हमारी आयु हे प्रभु, लोक के उपकार में, हाथ डालें हम कभी न, भूल कर अपकार में। कीजिए हम पर कृपा, ऐसी हे परमात्मा, मोह मद मत्सर रहित, होवे हमारी आत्मा। ॥ हे प्रभु आनंद-दाता ज्ञान हमको दीजिए...॥ प्रेम से हम गुरु जनों की, नित्य ही सेवा करें, प्रेम से हम संस्कृति की, नित्य ही सेवा करें। योग विद्या ब्रह्म विद्या, हो अधिक प्यारी हमें, ब्रह्म निष्ठा प्राप्त कर के, सर्व हितकारी बनें। ॥ हे प्रभु आनंद-दाता ज्ञान हमको दीजिए...॥ हे प्रभु आनंद-दाता ज्ञान हमको दीजिए, शीघ्र सारे दुर्गुणों को दूर हमसे ...

What do you know about sensitivity of a galvanometer? Define current sensitivity and voltage sensitivity of a galvanometer. Sensitivity of a galvanometer :  A galvanometer is said to be sensitive if a small current flowing through the coil of galvanometer produces a large deflection in the galvanometer. (i) Current Sensitivity : The current sensitivity of a galvanometer is defined as the deflection produced in the coil of the galvanometer per unit current flowing through it. That is, current sensitivity  $= \dfrac{\phi}{I} = \dfrac{\phi}{k \phi / (NAB)} = \dfrac{NAB}{k}$ Current sensitivity of galvanometer can be increased either by (a) increasing the magnetic field B by using a strong permanent horseshoe shaped magnet. (b) increasing the number of turns N of the coil. But, number of turns of the coil cannot be increased beyond a certain limit. This is because the resistance of the galvanometer will increase subsequently and hence the galvanometer becomes less sensitive. (c) i...

Lyrics : हर देश में तू, हर भेष में तू, Har Desh Mein Tu Har Bhesh Mein Tu - Param Himalaya  हर देश में तू, हर भेष में तू, तेरे नाम अनेक तू एक ही है, तेरे नाम अनेक तू एक ही है। तेरी रंगभूमि, यह विश्व भरा, सब खेल में, मेल में तू ही तो है॥ सागर से उठा बादल बनके, बादल से फटा जल हो करके। फिर नहर बना नदियाँ गहरी, तेरे भिन्न प्रकार, तू एक ही है॥ हर देश में तू, हर भेष में तू, तेरे नाम अनेक तू एक ही है, तेरे नाम अनेक तू एक ही है। चींटी से भी अणु-परमाणु बना, सब जीव-जगत् का रूप लिया। कहीं पर्वत-वृक्ष विशाल बना, सौंदर्य तेरा, तू एक ही है ॥ हर देश में तू, हर भेष में तू, तेरे नाम अनेक तू एक ही है, तेरे नाम अनेक तू एक ही है। यह दिव्य दिखाया है जिसने, वह है गुरुदेव की पूर्ण दया। तुकड़e कहे कोई न और दिखा, बस मैं अरु तू सब एकही है॥ हर देश में तू, हर भेष में तू, तेरे नाम अनेक तू एक ही है, तेरे नाम अनेक तू एक ही है। तेरी रंगभूमि, यह विश्व भरा, सब खेल में, मेल में तू ही तो है॥

Lyrics : हमको मन की शक्ति देना , Hum Ko Man Ki Shakti Dena - Param Himalaya  हमको मन की शक्ति, देना मन विजय करें दूसरों की जय से पहले खुद की जय करें हमको मन की शक्ति, देना मन विजय करें दूसरों की जय से पहले खुद की जय करें भेद-भाव अपने दिल से साफ़ कर सकें दूसरों से भूल हो तो माफ़ कर सकें झूठ से बचे रहें, सच का दम भरें दूसरों की जय से पहले खुद की जय करें हमको मन की शक्ति, देना मन विजय करें दूसरों की जय से पहले खुद की जय करें मुश्किलें पड़े तो हम पे, इतना कर्म करें साथ दे तो धर्म का, चलें तो धर्म पर खुदपे होसला रहे, बदी से ना डरें दूसरों की जय से पहले, खुद को जय करें

Lyrics : हम होंगे कामयाब, एक दिन , Hum Honge Kamyab Ek Din - Param Himalaya  हम होंगे कामयाब, हम होंगे कामयाब, हम होंगे कामयाब, एक दिन मन में है विश्वास, पूरा है विश्वास हम होंगे कामयाब एक दिन... होगी शांति चारों ओर, होगी शांति चारों ओर होगी शांति चारों ओर, एक दिन मन में है विश्वास, पूरा है विश्वास होगी शांति चारों ओर एक दिन... हम चलेंगे साथ-साथ डाल हाथों में हाथ हम चलेंगे साथ-साथ, एक दिन मन में है विश्वास, पूरा है विश्वास हम चलेंगे साथ-साथ एक दिन... नहीं डर किसी का आज नहीं डर किसी का आज, एक दिन मन में है विश्वास, पूरा है विश्वास नहीं डर किसी का आज एक दिन...

Lyrics : या कुन्देन्दुतुषारहारधवला , Ya Kundendu Tusharahara Dhavala  या कुन्देन्दुतुषारहारधवला या शुभ्रवस्त्रावृता, या वीणावरदण्डमण्डितकरा या श्वेतपद्मासना। या ब्रह्माच्युत शंकरप्रभृतिभिर्देवैः सदा वन्दिता, सा मां पातु सरस्वती भगवती निःशेषजाड्यापहा॥ शुक्लां ब्रह्मविचार सार परमामाद्यां जगद्व्यापिनीं, वीणा-पुस्तक-धारिणीमभयदां जाड्यान्धकारापहाम्‌। हस्ते स्फटिकमालिकां विदधतीं पद्मासने संस्थिताम्‌, वन्दे तां परमेश्वरीं भगवतीं बुद्धिप्रदां शारदाम्‌॥

Lyrics : इतनी शक्ति हमें देना दाता, Itanee shakti hamein denaa daata इतनी शक्ति हमें देना दाता, मन का विश्वास कमज़ोर हो ना हम चलें नेक रस्ते पे हमसे, भूलकर भी कोई भूल हो ना दूर अज्ञान के हो अँधेरे, तू हमें ज्ञान की रौशनी दे हर बुराई से बचके रहें हम, जितनी भी दे भली ज़िन्दगी दे बैर हो ना किसी का किसी से भावना मन में बदले की हो ना हम चलें नेक रस्ते पे हमसे भूलकर भी कोई भूल हो ना इतनी शक्ति हमें देना दाता, मन का विश्वास कमज़ोर हो ना हम न सोचें हमें क्या मिला है हम ये सोचें किया क्या है अर्पण फूल खुशियों के बांटें सभी को सबका जीवन ही बन जाए मधुवन अपनी करुणा का जल तू बहा के कर दे पावन हर एक मन का कोना हम चलें नेक रस्ते पे हमसे भूलकर भी कोई भूल हो ना इतनी शक्ति हमें देना दाता, मन का विश्वास कमज़ोर हो ना हर तरफ़ ज़ुल्म है, बेबसी है, सहमा सहमा सा हर आदमी है पाप का बोझ बढ़ता ही जाए, जाने कैसे ये धरती थमी है बोझ ममता से तू ये उठा ले, तेरी रचना का ये अंत हो ना हम चलें नेक रस्ते पे हमसे, भूल कर भी कोई भूल हो ना इतनी शक्ति हमें देना दाता, मन का विश्वास कमज़ोर हो ना हम अँधेरे में हैं रोशनी दे खो ना ...

Lyrics : वर दे, वीणावादिनी वर दे , Var De Veena Vadini Var De - सरस्वती वंदना Saraswati Vandana वर दे, वीणावादिनी वर दे। प्रिय स्वतंत्र-रव अमृत-मंत्र नव भारत में भर दे! वर दे, वीणावादिनी वर दे। काट अंध-उर के बंधन-स्तर बहा जननि, ज्योतिर्मय निर्झर कलुष-भेद-तम हर प्रकाश भर जगमग जग कर दे! वर दे, वीणावादिनी वर दे। नव गति, नव लय, ताल-छंद नव नवल कंठ, नव जलद-मंद रव; नव नभ के नव विहग-वृंद को नव पर, नव स्वर दे! वर दे, वीणावादिनी वर दे।

limitations of Ohm's law | Distinguish Ohmic and non ohmic circuit elements  Ohm's law is not considered to be a fundamental law. It explains the common behaviour of many substances/materials under given conditions like constant temperature and pressure. It is, therefore, possible that some materials may not strictly follow the Ohm's law (i.e. $V \propto I$). Ohm's law is not obeyed in the following cases : 1. When temperature of a conductor increases considerably . Ohm's law ($V \propto I$ or $R = \frac{V}{I}$) for a conductor at constant temperature is shown by a dotted line in Figure 13. However, when temperature of the conductor increase, its resistance increases and hence $V$ is not directly proportional to $I$. The behaviour of a conductor at high temperature is shown by a solid curve  2. Ohm's law is not obeyed by semiconductor diode. A semiconductor diode conducts, when forward biased and does not conduct, when reverse biased. (We shall discuss semicondu...

Drift of Electrons and the Origin of Resistivity :  Drift Velocity :  Consider a conductor with free electrons moving randomly. When an electric field $\vec{E}$ is applied across the conductor, the electrons experience a force $\vec{F} = -e\vec{E}$, where $-e$ is the charge of an electron. This force causes the electrons to accelerate. According to Newton's second law, $\vec{F} = m\vec{a}$, where $m$ is the mass of the electron and $\vec{a}$ is its acceleration. Therefore, $m\vec{a} = -e\vec{E}$ $\vec{a} = -\frac{e\vec{E}}{m}$ The electrons collide with the ions in the conductor. Let $\tau$ be the average time between successive collisions, known as the relaxation time. The average velocity acquired by the electrons due to the electric field is called the drift velocity $\vec{v}_d$. $\vec{v}_d = \vec{a}\tau = -\frac{e\vec{E}\tau}{m}$ The negative sign indicates that the drift velocity is opposite to the direction of the electric field. Origin of Resistivity :  Let $n$ be ...

Define Resistivity and conductivity | S.I Unit and Dimensions | Factors on depends Resistivity :  $\rho = R \left( \frac{A}{l} \right)$ If $A = 1$, $l = 1$, then $\rho = R$ resistivity of a conductor of a given material is defined as the resistance of the conductor of unit length and unit area of cross-section. S.I. Unit of Resistivity :  Since, $\rho = R \left( \frac{A}{l} \right)$, therefore, S.I. unit of $\rho$ is $\frac{\text{ohm metre}^2}{\text{metre}}$ or ohm-metre ($\Omega$ m) Dimensional formula of resistivity :  Resistivity, $[\rho] = \frac{[R] \times [A]}{[L]} = \frac{[ML^2T^{-3}A^{-2}] [L^2]}{[L]} = [ML^3T^{-3}A^{-2}]$ conductivity :  Electrical conductivity or conductivity of a substance is equal to the inverse of its resistivity. That is, $ \sigma = \frac{1}{\rho}$ S.I. unit of conductivity :  $\Omega^{-1} m^{-1}$ or $Sm^{-1}$. Dimensions of Conductivity :  $[\sigma] = \frac{1}{[\rho]} = [M^{-1}L^{-3}T^3A^2]$ $ \rho = \frac{m}{ne^2\tau$ $ and $...

Factor Affecting the Resistance: Electrical Resistivity or Specific Resistance State the factors on which the resistance of a conductor depends at constant temperature and hence define electrical resistivity or specific resistance. Give SI unit and dimensional formula of specific resistance. Resistance of a conductor at constant temperature depends upon: (a) Length of the conductor: The resistance R of a conductor is directly proportional to its length $l$. That is, $R \propto l \quad \ldots (i)$ More the length of a conductor, more is its resistance. (b) Area of cross-section of the conductor: The resistance of a conductor is inversely proportional to its area of cross-section A. That is, $R \propto \frac{1}{A} \quad \ldots (ii)$ Thus, thin wire has more resistance than the thick wire of same length. Combining eqns. (i) and (ii), we get $R \propto \frac{l}{A}$ or $R = \rho \left( \frac{l}{A} \right) \quad \ldots (iii)$ where, $\rho$ is known as specific resistance or resistivity of th...

Define Resistance and Conductance | SI Unit , Dimensions  Electric Resistance :  Resistance of a conductor is the opposition offered by the conductor to the flow of electric charge in the conductor. Resistance of a conductor is defined as the ratio of the potential difference across the ends of the conductor to the current flowing through it. That is, $R = \frac{V}{I}$ S.I. unit of resistance :  It's S.I unit is ohm ($\Omega$) $1 \text{ ohm } (\Omega) = \frac{1 \text{ volt } (V)}{1 \text{ ampere } (A)} \quad \text{ or } 1 \Omega = 1 VA^{-1}$ Definition of 1 ohm:  Resistance of a conductor is said to be 1 ohm, if current of 1 A flows through it, when potential difference of 1 V is applied across it. Dimensional formula of resistance: $[R] = \frac{[V]}{[I]}$ $[R]= \frac{[\text{Work}]}{[\text{Charge}] \times [\text{Current}]}$ $[R]=\frac{[\text{Work}]}{[\text{Current}] \times [\text{Time}] \times [\text{Current}]}$ $= \frac{[ML^2T^{-2}]}{[A^2T]}$ $= [ML^T^{-3}A^{-2}]$ C...

State and Verify Ohm's Law | Draw V-I Characteristics - Param Himalaya  Statement of Ohm's Law :  According to Ohm's law, the current ($I$) flowing through a conductor is directly proportional to the potential difference ($V$) across the ends of the conductor, provided the physical conditions (like temperature, pressure, strain, etc.) of the conductor remain unchanged. Mathematically, this can be expressed as: $V \propto I$ Introducing a constant of proportionality, $R$, known as the electric resistance or simply resistance of the conductor, we get: $V = RI$ This can also be written as: $R = \frac{V}{I}$ The value of $R$ depends on the nature of the material of the conductor, its dimensions, and temperature. It does not depend on the values of $V$ and $I$. Verification of Ohm's Law :  Ohm's law can be verified using the voltmeter-ammeter method. A circuit is set up with a battery connected to a conductor XY through a rheostat, an ammeter in series, and a key. A volt...

RESISTIVITY OF VARIOUS MATERIALS For ideal conductor, resistivity is zero and for ideal insulator , the resistivity is infinite.  Metals have low resistivities in the range of $10^{-8} \Omega m$ to $10^{-6} \Omega m$. At the other end are insulators like ceramic, rubber and plastics having resistivities $10^{18}$ times greater than metals or more. In between the two are the semiconductors. These, however, have resistivities characteristically decreasing with a rise in temperature. The resistivities of semiconductors can be decreased by adding small amount of suitable impurities.  Resistivity of material is inversely proportional to its conductivity therefore conductivity of conductor is more than that of semiconductor. the conductivity of a semiconductor is more that of an insulator

Discuss the temperature dependence of resistivity of metals/conductors, insulators and semiconductors. It has been observed that at low temperature, resistivity of a conductor increases at a higher power of temperature (T). Thus, over a limited range of temperature, the variation of $\rho$ with temperature (T) is expressed by the relation $\rho = \rho_0 [1 + \alpha (T - T_0)]$ where $\rho_0$ is the resistivity at reference temperature $T_0$ (say 273 K or $0^\circ$C), $\rho$ is resistivity at temperature $T$ and $\alpha$ is the temperature coefficient of resistivity. The temperature coefficient of resistivity is defined as : $\alpha = \frac{(\rho - \rho_0)}{\rho_0 (T - T_0)} = \frac{\Delta \rho}{\rho_0 \Delta T}$ Thus, temperature coefficient of resistivity ($\alpha$) is defined as the change in resistivity per unit original resistivity per unit change in temperature. The SI unit of temperature coefficient of resistivity is (kelvin)$^{-1}$ or K$^{-1}$. Temperature coefficient of resisti...

Define electric energy and power. Give their S.I. units and define them. Give relation between them. Electric Energy : The work done by a source to maintain a current in an electrical circuit is known as electric energy. Consider an electric device or circuit element (e.g., an electric lamp, heater etc.) of resistance $R$ through which current $I$ flows from the end $A$ to the end $B$ for time $t$. Let $q$ be the charge flowing from $A$ to $B$ in time $t$, then $q = It \quad \left( I = \frac{q}{t} \right)$ If $V$ be the potential difference between $A$ and $B$, then work done to carry the charge $q$ from point $B$ to $A$ is equal to the change in potential energy of the charge $q$ and is given by  $W = \Delta U = Vq = VIt$ This work done is equal to the electric energy $E$ consumed in the circuit and is given by E = VIt We know, $V = IR$ (from Ohm's law) $E = (IR) It = I^2Rt = \left( \frac{V}{R} \right)^2 Rt = \frac{V^2}{R} t$ This electric energy appears as heat energy in the res...

Define cell, e.m.f., terminal potential difference and internal resistance of a cell. A cell is a device which provides the necessary potential difference to an electric circuit to maintain a continuous flow of current in it. A cell consists of two rods or plates called electrodes which are dipped in a chemical solution called electrolyte. The pictorial symbol of a cell is $\dashv \vdash$. Longer vertical line shows +ve terminal and shorter vertical line shows -ve terminal of the cell. (a) EMF (Electromotive force) :  E.M.F. of a cell may be defined as the potential difference between the terminals of the cell when no current is drawn from the cell. In a cell, the positive charges are driven towards an electrode making it positive and the negative charges towards the other electrode making it negative. Thus, a potential difference develops between +ve and -ve electrodes i.e. terminals of the cell. E.M.F. of a cell can also be defined as: The work per unit charge done by a cell in m...

CELLS IN SERIES AND PARALLEL :  Derive expressions for equivalent e.m.f. and internal resistance of cells connected in series, parallel and mixed combination. Cells can be connected in : (i) series, (ii) parallel, (iii) mixed combination. Cells Connected in Series :  In series combination of the cells, the negative terminal of a cell is connected to the positive terminal of an other cell, and so on. (a) Identical Cells Connected in Series:  Consider $n$ identical cells such as $C_1$, $C_2$, $\dots$, $C_n$ each of e.m.f. $\varepsilon$ and internal resistance $r$ connected in series to an external resistance $R$. Since cells are connected in series, so the total e.m.f. of $n$ cells = $n\varepsilon$. That is,     $\varepsilon_{\text{eff}}= \varepsilon + \varepsilon + \varepsilon + \dots n = n\varepsilon$     $r_{\text{eff}} = r + r + r + \dots \text{upto } n \text{ terms} = nr$ Total resistance = $r_{\text{eff}} + R$ Total resistance = $nr + R$ Hence, eqn...

KIRCHHOFF'S LAWS AND SIMPLE APPLICATIONS :  Question : State and explain Kirchhoff's rules with the help of simple applications. Kirchhoff's laws are used to find the currents and voltages in different parts of the circuit. Kirchhoff's First Law or Rule (The Junction Law or Kirchhoff's Current Law) :  It states that the sum of all the currents entering any point (or junction) must be equal to the sum of all currents leaving that point (junction). The algebraic sum of all the currents meeting at a point (or junction) in a closed electrical circuit is zero. That is, $ \Sigma I = 0 $ Consider a point or junction O in an electrical circuit (Figure 37). Let $I_1$, $I_3$ be the currents entering the point O and $I_2$, $I_4$, $I_5$ be the currents leaving the point O. Then according to Kirchhoff's first law or junction law, $I_1 + I_3 = I_2 + I_4 + I_5 \quad \dots(i)$ or $ I_1 + I_3 + (-I_2) + (-I_4) + (-I_5) = 0 $ or $ I_1 + I_3 - I_2 - I_4 - I_5 = 0$ or  $\Sigma I = ...

What is Wheatstone bridge? Give its principle, theory and proof. Wheatstone bridge is an arrangement of four resistors in the form of a bridge used for measuring one unknown resistance in terms of other three known resistances Construction : Four resistors of resistances $P, Q, R$ and $S$ respectively are arranged in the form of a bridge. A source of e.m.f. '$\epsilon$' is connected between points $A$ and $C$. A galvanometer is connected between points $B$ and $D$. Unknown resistance can be in any of the four arms of the bridge $P, Q, R$ and $S$. Usually, unknown resistance is Put at S. Out of the four resistances, one(S) is unknown, one is variable (R) and the other two (P and Q) can be standard resistors. Principle : When key K is closed, the galvanometer shows the presence of current $I_g$ through it. The value of a resistances say R is adjusted in such a way that the galvanometer shows no deflection. At this stage, the potential at points B and D is equal and hence no curr...

Coherent and Incoherent Addition of Waves  When two identical vibrating needles are allowed to oscillate in phase when they just touch the free surface of water in the tank at points $S_1$ and $S_2$. These needles generate two waves, each of amplitude $A$ at any instant. Phase difference between their displacement does not change with time. Consider a point $P$ such that $S_1P = S_2P$. At this point, resultant displacement is the sum of the individual displacements $y_1$ and $y_2$ of the two waves respectively. $y = y_1 + y_2 \quad \dots (i)$ $But \quad y_1 = y_2 = A \sin \omega t$ $\therefore \quad y = 2A \sin \omega t$ where $2A$ is the amplitude of the resultant wave. Now, intensity, $I \propto (\text{amplitude})^2$ $\therefore$ resultant intensity, $\quad I = K(2A)^2 = 4KA^2 = 4I_0$ $I_0 = KA^2$ is the intensity of wave produced by each source.  Thus, the intensity of the resultant wave at any point on the perpendicular bisector of $S_1S_2 = 4I_0$. Now, consider another po...

Derivation : Law of Reflection and Refraction by Huygens Principle (Snell's law)  - Param Himalaya  Derivation of Laws of Refraction (Snell's law) from Huygens' Principle  (i) Plane wavefront refracted in denser medium :  AB is an incident wavefront striking the interface XY at point A. Refractive index of medium II is greater than refractive index of medium I, $n_2>n_1$. Let $v_1$ be speed of light in medium I and $v_2$ be the speed in medium II ($v_2 < v_1$). According to Huygens' principle, every point on incident wavefront AB acts as a source of disturbance. Time in which wavelet reaches from B to C is given by $t = \frac{BC}{v_1} \quad \text{i.e.,} \quad BC = v_1 t$ Draw AD = $v_2 t$ to get a point on the secondary spherical wavefront originating from point A on the incident wavefront. Join CD. Therefore, CD is the refracted wavefront. $\frac{BC}{AD} = \frac{v_1}{v_2} \quad \dots (i)$ In $\triangle BAC, \quad BC = AC \sin i$  and In $\triangle ACD, \q...