Formulae for Physics CBSE Class 12 Session 2023-24, Cheat Sheet of Physics

Download Formulae for Physics CBSE Class 12 Session 2023-24 and more Cheat Sheet Physics in PDF only on Docsity! CLASS 12 BOOK 2 - FORMULA SHEET RAY OPTICS Reflection  Angle of incidence = angle on reflection  R = 2f  Mirror formula 1 1 1 v u f    Magnification, image object h m h   Also v m u   1 1 1 v u f u u u v u f 1 u 1 m f 1 u 1 m f f m f u                 Refraction  Refractive index Absolute refractive index m m c μ c  Relative refractive index 1 1 2 2 c μ c  1 1 2 2 1 1 1 2 2 2 c νλ , c νλ , νλ λ μ νλ λ     Also, 1 2 2 1 μ μ μ   Snell’s law 1 2μ sini μ sinr  Real depth and apparent depth Real depth μ Apparent depth   Total internal reflection c 1 μ sini   Refraction at a spherical surface Rarer to denser 2 1 2 1μ μ μ μ v u R    Denser to rarer 1 2 1 2μ μ μ μ v u R     Lens makers’ formula 2 1 1 2 μ1 1 1 1 f μ R R            For convex lens 1 2 R ve R ve     For concave lens 1 2 R ve R ve      Thin lens formula Compound microscope o o e v D m 1 u f        Normal adjustment o o e v D m u f        Length of microscope tube o eL v | u |  Astronomical telescope o e f m f   WAVE OPTICS Interference of light: young’s double slit experiment     1 2 y asin ωt y bsin ωt φ    After interference, the amplitude R of the resultant wave is 2 2R a b 2abcosφ    2 2 2 2 1 2 2 2 2 1 2 1 2 1 21 2 1 2 1 2 Intensity Amplitude I a , I b , I R R a b 2abcosφ I I I II 2 cosφ k k k k k I II II 2 cosφ k k k 2 I I I 2 I I cosφ                            If intensity of both sources is same (let Io), then 2 o φ I 4I cos 2  2 1 1 2 2 2 I ωa I b ω   Constructive interference For intensity of light to be maximum at P, cosφ = 1 phase difference φ = 2nπ , where n = 0,1,2,3,4........ 2π φ x λ 2π 2nπ x λ x nλ     Destructive interference For intensity of light to be minimum at P, cosφ 1 φ (2n 1)π 2π x (2n 1)π λ λ x (2n 1) 2         Ratio of intensity of light at Maxima and minima 2 max 1 2 2 min 1 2 I ( ) I ( )    a a a a Ratio of intensity of light due to two sources Let I1 and I2 and a1 and a2 be the intensities and amplitudes of light from slits S1 and S2 respectively. Then, 2 1 1 2 2 2 I a = I a Relation between slit width (), I and a 2 1 1 1 2 2 2 2 ω I a = = ω I a Position for maxima and minima n ' distance of n th brigh t fringe from centre of screen , nλD y = , d d istance of n th dark fringe from centre of screen , (2n + 1 )λD , 2d w here n 0,1, 2,3 ......   ny Linear width of each fringe λD d The angular width of each fringe, β λ Δθ = = D d Single slit diffraction ATOMS Velocity of an electron 22πkZe v nh  1 v c 137       Radius of the orbit of electron 2 2 2 2 2 nh nh r . 2πm 2πkZe n h r 4π mkZe    ENERGY Kinetic energy of electron in nth orbit 2 21 kZe K.E mv 2 2r   [Using equation (i)] Potential energy of electron in nth orbit is 2 1 2q q (Ze)( e) Ze P.E k k k r r r      Total energy T.E = P.E + K.E 2 2 2Ze Ze Ze T.E k k k 2r r 2r     Putting the value of r, we get 2 2 2 2 2 kZe 4π mkZe T.E . 2 n h   2 2 2 4 2 2 2π mk Z e T.E n h    Wavelength of emitted photon when an electron comes back from higher energy (n2) state to lower energy state (n1). 2 2 1 2 2 2 4 3 1 1 1 R λ n n 2π mk e where R , is the Rydberg constant ch          Value of R is 1109733 cm NUCLEI Radius of a nucleus 1/3 oR R A Density of nucleus Volume of nucleus 3 31 3 o o 4 R 3 4 4 R A R A 3 3            Therefore, nuclear density Mass of nuclues Volume of nucleus   3 3 o o mA 3m 4 4 RR A 3     17 32.30 10 kgm   Nuclear binding energy     p n N 2 Mass defect, m Zm (A Z)m m E m c        Multiply m (in amu) by 931 to get answer in MeV. Binding energy Binding energy per nucleon mass number  m Packing fraction A  