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Ray Optics - Kirne Prakashiki Ray Optics yaani Kirne Prakashiki , light ke straight line propagation (seedhi rekha mein chalna) aur reflection (paravartan) & refraction (apavartan) ko study karta hai. JEE ke liye bohot important topic hai, basic concepts strong hone chahiye. Reflection (Paravartan) - Jab Light Takra Ke Vaapas Aaye Laws of Reflection (Paravartan ke Niyam) Angle of incidence ($i$) is equal to the angle of reflection ($r$). Yani, $i = r$. Incident ray, reflected ray, aur normal (surface ke perpendicular line) sab ek hi plane mein hote hain. i r Normal Incident Reflected Plane Mirror (Samtal Darpan) Image virtual (aabhasi), erect (seedha), aur laterally inverted (paarsvik ulta) banti hai. Image distance ($v$) = Object distance ($u$). Yani, $|v| = |u|$. Magnification ($m$) = 1. (Image size = Object size). Agar mirror $\theta$ angle se rotate kare, toh reflected ray $2\theta$ angle se rotate karti hai. Do plane mirrors ke beech multiple images: Agar objects mirrors ke symmetric ho, toh number of images $N = \frac{360^\circ}{\theta} - 1$. Agar objects asymmetric ho, toh $N = \frac{360^\circ}{\theta}$ (agar $\frac{360^\circ}{\theta}$ integer ho) ya $N = \text{floor}(\frac{360^\circ}{\theta})$ (agar $\frac{360^\circ}{\theta}$ integer na ho, aur object beech mein ho). Spherical Mirrors (Goliya Darpan) - Concave (Avatal) & Convex (Uttal) Sign Convention (Chinh Parampara): Generally, New Cartesian Sign Convention use karte hain. Pole (P) ko origin maano. Incident light ki direction mein distances positive, opposite direction mein negative. Principal axis ke upar positive, neeche negative. Mirror Formula (Darpan Sutra): $$ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} $$ Jahan: $f$ = Focal length (focal doori) $v$ = Image distance (pratibimb doori) $u$ = Object distance (vastu doori) Magnification (Aavardhan): $$ m = \frac{h_i}{h_o} = -\frac{v}{u} $$ Jahan: $h_i$ = Height of image $h_o$ = Height of object Focal length ($f$) aur Radius of Curvature ($R$): $$ f = \frac{R}{2} $$ Concave mirror ke liye $f$ negative, convex mirror ke liye $f$ positive. Mirror Type $f$ Image Nature (Real Object) Concave (Avatal) Negative Depends on object position (Real/Virtual) Convex (Uttal) Positive Always Virtual, Erect, Diminished Refraction (Apavartan) - Jab Light Medium Change Kare Laws of Refraction (Apavartan ke Niyam) Incident ray, refracted ray, aur normal (interface ke perpendicular line) sab ek hi plane mein hote hain. Snell's Law: For a given pair of media and for a given color of light, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. $$ n_1 \sin i = n_2 \sin r $$ Jahan: $n_1$ = Refractive index of medium 1 $n_2$ = Refractive index of medium 2 $i$ = Angle of incidence $r$ = Angle of refraction Refractive Index ($n$): Medium mein light ki speed air/vacuum mein light ki speed se kitni kam hai, ye batata hai. $$ n = \frac{c}{v} $$ Jahan $c$ = speed of light in vacuum, $v$ = speed of light in medium. Apparent Depth (Aabhasi Gehrai) Agar aap dense medium se rare medium ki taraf dekhte ho (e.g., paani ke andar se bahar), toh object apni actual position se thoda upar dikhta hai. $$ d_{apparent} = \frac{d_{real}}{n_{relative}} $$ Agar air se paani mein dekh rahe ho, toh $n_{relative} = n_{water}/n_{air} \approx n_{water}$. $$ d_{apparent} = \frac{d_{real}}{n} $$ Total Internal Reflection (TIR) - Purn Aantarik Paravartan Light denser medium se rarer medium mein travel kar rahi ho. Angle of incidence ($i$) critical angle ($\theta_c$) se zyada ho. Critical Angle ($\theta_c$): $$ \sin \theta_c = \frac{n_{rarer}}{n_{denser}} $$ Examples: Optical fibers, mirage, diamond ki chamak. Refraction at Spherical Surfaces (Goliya Satahon par Apavartan) Formula: $$ \frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R} $$ Jahan: $n_1$ = Medium ka refractive index jahan object hai. $n_2$ = Medium ka refractive index jahan light refract hone ke baad jaati hai. $u$ = Object distance. $v$ = Image distance. $R$ = Radius of curvature (sign convention ke saath). Lenses (Lens) - Light ko Bend Karna Lens Maker's Formula (Lens Nirman Sutra) $$ \frac{1}{f} = (n_{lens} - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) $$ Jahan: $f$ = Focal length. $n_{lens}$ = Lens material ka refractive index (relative to surrounding medium, usually air). $R_1$, $R_2$ = Radii of curvature of the two lens surfaces (sign convention ke saath). Thin Lens Formula (Patla Lens Sutra) $$ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $$ Magnification ($m$): $$ m = \frac{h_i}{h_o} = \frac{v}{u} $$ Power of a Lens ($P$): Lens ki light ko bend karne ki capacity. $$ P = \frac{1}{f \text{ (in meters)}} $$ Unit = Diopter (D). Converging lens (convex) ki power positive, diverging lens (concave) ki power negative. Combination of Lenses (Lenses ka Sanyojan) Agar do thin lenses contact mein hain, toh equivalent focal length $F_{eq}$: $$ \frac{1}{F_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} $$ Equivalent power $P_{eq}$: $$ P_{eq} = P_1 + P_2 $$ Lens Type $f$ Image Nature (Real Object) Convex (Uttal) Positive Depends on object position (Real/Virtual) Concave (Avatal) Negative Always Virtual, Erect, Diminished Prism (Prism) - Light ka Dispersion Deviation Angle ($\delta$): Light ray kitne angle se bend hui. $$ \delta = (i_1 + e) - A $$ Jahan: $i_1$ = Angle of incidence. $e$ = Angle of emergence. $A$ = Angle of prism. Minimum Deviation ($\delta_m$): Jab $i_1 = e$ aur $r_1 = r_2 = r$. $$ \delta_m = 2i - A $$ $$ n = \frac{\sin \left( \frac{A + \delta_m}{2} \right)}{\sin \left( \frac{A}{2} \right)} $$ Dispersion: White light ka apne constituent colors mein split hona (VIBGYOR). Optical Instruments (Prakashik Yantra) Human Eye (Manav Netra) Near Point: 25 cm (normal eye ke liye). Far Point: Infinity. Defects: Myopia (nearsightedness - concave lens), Hypermetropia (farsightedness - convex lens), Presbyopia (bifocal lens), Astigmatism (cylindrical lens). Simple Microscope (Saral Sukshmadarshi) - Magnifying Glass Angular Magnification ($M$): Image at Near Point (25 cm): $M = 1 + \frac{D}{f}$ Image at Infinity: $M = \frac{D}{f}$ Jahan $D = 25 \text{ cm}$. Compound Microscope (Sanyukt Sukshmadarshi) Total Magnification ($M_{total}$): $$ M_{total} = m_o \times M_e $$ Jahan $m_o = -\frac{v_o}{u_o}$ (objective lens ka magnification) aur $M_e$ (eyepiece ka angular magnification). Image at Near Point: $M_{total} = \left( \frac{L}{f_o} \right) \left( 1 + \frac{D}{f_e} \right)$ Image at Infinity: $M_{total} = \left( \frac{L}{f_o} \right) \left( \frac{D}{f_e} \right)$ Jahan $L$ = length of microscope tube ($v_o + u_e$). Astronomical Telescope (Khagoliya Durdarshi) Angular Magnification ($M$): Image at Near Point: $M = -\frac{f_o}{f_e} \left( 1 + \frac{f_e}{D} \right)$ Image at Infinity (Normal Adjustment): $M = -\frac{f_o}{f_e}$ Length of telescope tube: Image at Near Point: $L = f_o + u_e$ Image at Infinity: $L = f_o + f_e$ Important JEE Tips Sign Convention: Iska bohot dhyan rakho. Ek galti poora answer galat kar sakti hai. Ray Diagrams: Practice karo, ye conceptual clarity badhate hain. Formulae Yaad Rakho: Saare formulae by heart hone chahiye, especially mirror/lens/prism/TIR ke. Previous Year Questions: PYQs solve karne se exam pattern aur important topics ka idea lagta hai. Approximations: Small angle approximations ($\sin \theta \approx \theta$, $\tan \theta \approx \theta$) ka use bohot hota hai.