d sinθ = mλ Interference and diffraction double slit or diffraction grating d sinθ = mλ d sinθ is the path difference x (small angle approximation)

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1 Wave Optics Wave prperties f light The clrs in a rainbw are ROY G. BIV (Red, range, yellw, green, blue, indig, vilet). White light is a cmbinatin f all clrs Black is the absence f light Wavelength determines clr ( red is stretch and spread, blue is clse yu, and green is in between ) Humans can see light with wavelengths between 400nm (vilet) 700nm (red) Amplitude determines brightness Light is a transverse wave. This is prved by plarizatin destructive interference ccurs when the path difference is half integer # f wavelengths diffractin grating has narrwer/sharper fringes than duble slit (see diagram) single slit d sinθ = mλ mλl x (small angle apprximatin) d bright fringes/cnstructive interference at m=0,1.5,2.5,... dark areas/destructive interference at m=1,2,3.. Has wider central max than duble slit (see diagram) Electrmagnetic waves Light is part f a wave family called the Electrmagnetic Spectrum Electrmagnetic waves, frm lwest t highest energy (and frequency), are: Radi waves Micrwaves Infrared waves Visible light waves Ultra vilet waves X-rays Gamma waves All electrmagnetic waves travel at the same speed (c) which is 3.0 x 10 8 m/s Electrmagnetic waves d nt require a medium t travel thrugh. (Hwever, they can travel thugh a medium like air r glass r water t. They just dn t need a medium. Sund is different. Sund needs a medium t prpagate.) The length f the mst effective transmitting antenna is equal t ne furth the wavelength f the bradcast wave. If a radi statin has an antenna 4.5 meters lng then what is the bradcast frequency f the radi statin? A) 1.4 x 10 8 Hz B) 6.0 x 10 8 Hz C) 1.7 x 10 7 Hz D) 6.7 x 10 7 Hz E) 3.0 x 10 8 Hz In Yung s duble slit experiment, the secnd rder bright band f ne light surce verlaps the third rder band f anther light surce. If the first light surce has a wavelength f 660 nm, what is the wavelength f the secnd light surce? A) 1320 nm B) 990 nm C) 495 nm D) 440 nm E) 330 nm Interference and diffractin duble slit r diffractin grating d sinθ = mλ d sinθ is the path difference mλl x (small angle apprximatin) d bright fringes/cnstructive interference at m=0,1,2,3.. dark areas/destructive interference at m=0.5,1.5,2.5.. cnstructive interference ccurs when the path difference is an integer # f wavelengths

2 In a Yung's duble-slit experiment, the slit separatin is dubled. T maintain the same fringe spacing n the screen, the screen-t-slit distance D must be changed t A) D/2 B) D 2 C) 2 D D) 2D E) 4D Ray Optics Reflectin Law f reflectin: Incident angle equals reflected angle The image frm a plane mirrr is virtual, and has the same rientatin, size, and distance frm the mirrr as the bject Thin film interference 2T = mλ n T is the thickness f the film, λ is the wavelength in the film: λ n =λ/n 180 phase change if reflect ff slwer medium (higher n) n phase change when reflect ff faster medium (lwer n) if TWO phase changes cnstructive: m=0,1,2,3.. destructive: m=0.5,1.5,2.5.. if ONE phase change cnstructive: m=0.5,1.5,2.5.. destructive: m=0,1,2,3.. Frequency is cnstant in a new medium! A light ray is incident nrmal t a thin layer f glass. Given the figure, what is the minimum thickness f the glass that gives the reflected light an rangish clr (λ(air) range light = 600nm) A) 50 nm B) 100 nm C) 150 nm D) 200 nm E) 500 nm Refractin Light changes speed in different media as determine by the index f refractin (n) c v= n n air =1, n water =1.33, n glass =1.5, n diamnd =2.41 When light changes speeds, it als changes directin. The farther it bends frm the nrmal line, the faster it travels. Which medium has a greater speed f light? Which medium has a greater index f refractin? Medium 1 Medium 2 n 1sinθ1 = n2sinθ - Snell s law relates incident and 2 reflected angle Ttal internal reflectin can ccur when ging frm slwer t faster medium, and refracted angle is 90 degrees. The incident angle is called the critical angle in this case. The diagram belw shws the path taken by a mnchrmatic light ray traveling thrugh three media. The symbls v 1, λ 1, and f 1 represent the speed, wavelength, and frequency f the light in Medium 1, respectively. Which f the fllwing relatinships fr the light in the three media is true?

3 Cncave Mirrrs Cnvex Lens ` c f 2f f smaller smaller same size same size N image N image virtual - upright virtual - upright distant bjects create parallel rays f stands fr fcal pint c stands fr center f curvature (c=2f) 3 rules In parallel, ut fcus In fcus, ut parallel In center, ut center images frmed where reflected rays cnverge virtual images are upright, real images are inverted as bject gets clser, image gets further at c bject and image are same size and distance image when bject is between c and f NO IMAGE is frmed at f because reflected rays are parallel Inside f nly virtual images frmed = + If I d, I die f d d i h i d = i h d distant bjects create parallel rays f stands fr fcal pint Treat 2f like c fr curved mirrrs 3 rules In parallel, ut fcus In fcus, ut parallel In center, ut center images frmed where refracted rays cnverge real images are inverted and n ppsite side virtual images are upright and n same side as bject gets clser, image gets further at 2f bject and image are same size and distance image when bject is between 2f and f NO IMAGE is frmed at f because refracted rays are parallel Inside f nly virtual images frmed = + If I d, I die f d d i h i d = i h d

4 Phtn absrptin indicated by upward arrws n energylevel diagrams electrns emit phtns when they fall back dwn t lwer energy levels. Phtn emissin indicated by dwnward arrws n energylevel diagrams. The larger the gap between energy levels, the higher the phtn s frequency, and vice versa. An electrn can becme inized (break away frm the nucleus) if it absrbs enugh energy. The energy f a phtn can be calculated using E=hf (h = 4.14E-15 ev-s) f can be replaced using the speed f a wave equatin: E hf = hc λ = (hc = 1240 ev-nm) The diagram shws the lwest fur energy levels fr an electrn in a hypthetical atm. The electrn is excited t the 1 ev level f the atm and transitins t the lwest energy state by emitting nly tw phtns. Which f the fllwing energies culd nt belng t either f the phtns? (A) 2 ev (B) 4 ev (C) 5 ev (D) 6 ev (E) 9 ev Atms and Phtns 4 th excited state 3 rd excited state 2 nd excited state 1 st excited state Electrns are fund utside the nucleus, but nly at specific distances frm the nucleus, called shells, rbitals, energy levels, r states. Electrns cannt exist between these energies The energy level clsest t the nucleus is called the grund state and has the lwest energy. All states have negative energy (remember: we can set PE t be zer anywhere) Electrn-vlts (ev) is cmmnly used as a unit f energy because we re dealing with electrns. Electrns get excited t higher energy levels by absrbing phtns Which f the fllwing transitins will prduce the phtn with the lngest wavelength? (A) n = 2 t n = 1 (B) n = 3 t n = 1 (C) n = 3 t n = 2 (D) n = 4 t n = 1 (E) n = 4 t n = 3

5 Nuclear Decay Charge is cnserved in any nuclear reactin Alpha decay: 2 prtns and 2 neutrns (Helium nucleus) released frm nucleus Beta decay: Beta minus: electrn released frm nucleus, neutrn turns int prtn Beta plus: psitrn released frm nucleus, prtn turns int neutrn Gamma decay: high energy electrmagnetic radiatin emitted What des the? represent in the nuclear reactin 2 H H 1 3 He 2 +? A) an alpha B) a beta C) a gamma D) a neutrn E) a prtn During a particular kind f radiactive decay, a particle is emitted frm the nucleus f an atm and the atm s atmic number increases by ne. This decay necessarily invlves the emissin f frm the nucleus A) an alpha particle B) a beta particle C) a gamma ray D) a prtn E) a neutrn