Notes for the Physics GRE - Harvard University Department of Physics

where d is now the distance between slits. This equation also applies to diffractiongratings. For Bragg diffraction,For a film of thickness t,For a telescope,2d sin θ = λ. (156)2t = λ/2 ⇒ constructive interference, (157)2t = λ ⇒ destructive interference. (158)Magnetization = f Of e, (159)where f O is the focal length of the objective lens and f e is the focal length of theeyepiece. The distance between the objective lens and the eyepiece is f O + f e .The aperture formula:θ = 1.22λ/d. (160)Here, θ is the angular aperture, d is the diameter of the lens, and λ is thewavelength.The E-field for a light wave traveling in the z-direction can be written as,⃗E(⃗r, t) = (A x cos(kz − ωt), A y cos(kz − ωt + φ), 0). (161)If φ = 0, π, the light is linearly polarized, and the direction depends on theamplitudes, A x , A y . If φ = π/2, −π/2 and A x = A y , the light is circularlypolarized. Otherwise, the light is elliptically polarized. A polarizer allows onlycertain polarizations of light to pass through. The intensity I of the waveemerging from the polarizer is related to the incoming intensity I 0 and theangle θ between polarization and polarizer by,I = I 0 cos 2 θ. (162)If the incoming light is unpolarized, I = I 0 /2. The B-field is perpendicular toboth the direction of propagation and the E-field.The Doppler effect for sound is,( ) v + vrω obs = ωem . (163)v + v sHere, v is the speed of sound, v r is the speed of the receiver, and v s is the speed ofthe source. The sign convention can be determined by remembering that movingcloser corresponds to a blueshift (greater bserved frequency) and moving apartcorresponds to a redshift (lesser observed frequency). Note that a blowing winddoesn’t affect v r or v s , since the time of propagation for consecutive pulses isnot changing with time.23