l. For adjacent fringes, m dsin m

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1 Test 3 Pratie Problems Ch 4 Wave Nature of Light ) Double Slit A parallel beam of light from a He-Ne laser, with a wavelength of 656 nm, falls on two very narrow slits that are mm apart. How far apart are the fringes in the enter of the pattern on a sreen 4. m away? For onstrutive interferene, the path ifferene is a multiple of the wavelength. The loation on the sreen is given by x l tan, For small angles, we have sin tan x l. For ajaent fringes, m. x ml sin m m x l m 3.8m l x m 0.035m 3.5m m 9 l (656x0 m)(4.m) x m ) m ( (0.050x0 3 m) ) Single Slit In an experiment you shine re light of wavelength 533 nm on a slit, generating a entral iffration peak of θ = 8.4 o as shown in the figure. How wie is the slit? The first ark fringe happens when: 533nm Dsin so: D sin sin µm 3) Diffration Grating A iffration grating has lines separate by 3.5 μm. Calulate the angle of iffration of the first orer fringe for green light (λ = 530 nm) an re light (λ = 650 nm). The equation that esribes iffration gratings is: Sin m If we are looking for the first fringe m=, so: Sin For the given wavelengths we get: 530nm (a) Green light θ Sin 8.7º 35. μm 650nm (b) Re light θ Sin 0.7º 35. μm

2 4) Diffration Grating A iffration grating is use to etermine wavelengths in a spetrometer. Calulate the angular separation (in egrees) between the two main lines of soium (589.0 nm an nm) if the grating has a ensity of 5,000 lines per inh. [ inh =.54 m] The ensity of lines implies a istane between slits of: inh 5000lines.54x0 m.6933x0-6 m 5000lines To get the angular separation we will fin the angle for eah wavelength an alulate the ifferene: sin( ) sin x0 m sin 0.355º x x0 m sin 0.376º x0 So the ifferene is 0.0º 5) Polarization Fin how muh intensity of a beam of un-polarize light will go through three polarizers, where the first an seon are rotate 37 o with respet to eah other an the seon an thir are also rotate 37 o with respet to eah other. If you start with unpolarize light of intensity I o, after the first polarizer you will have polarize light of intensity Io, the seon polarizer is rotate by 37 o, so there will be aitional losses, the thir polarizer is also rotate by 37 o, an the final intensity will be: I FINAL 4 o Io[Cos (37 )] 0.03 I o 0.3% of I o Ch 5 - ptial Instruments 6) Nearsighte/Farsighte Corretion. Alie is nearsighte with a far point of 5 m (she annot see learly beyon this point). What kin of glasses an of what power oes she nee to see istant objets learly? [Neglet eye-lens istane in this problem]. To bring istant objets (o= ) to the far point we nee i to be equal to -0.5m, the minus sign beause we want the image in front of the person, not behin her hea. So the power will be: f o i 0. 5m -4D Sine the power is negative, this lens is a iverging lens.

3 7) Limit of Resolution A amera has an objetive lens 5 m in iameter. a) Calulate the minimum angle between two points that will still be istinguishe in the piture. Consier that the wavelength is λ = 590 nm. b) Knowing the minimum angle an knowing that the istane from the two points to the amera is 50 m, how lose an the points be an still be istinguishe? a) sin x0-4 egrees Diameter b) x Lsin mm 8) Telesope/Mirosope A telesope has an objetive with foal length 75 m an a +5-D eyepiee. magnifiation? What shoul be the length of the telesope? What is the total The magnifiation of the telesope is given by Eq M fo (75m) 9x f (4.0m) e For both objet an image far away, the separation of the lenses is the sum of the foal lengths. fo + fe = = 79 m Ch 6 Speial Theory of Relativity 9) Time Dilation A partile has a lifetime of ns in its own rest frame, but it overs a istane of.6 m in the laboratory before eaying. How fast is it moving? We use the equation that we learne in Physis I, but we use the ilate time in the equation: t v To T o v From the point of view of physis the problem is solve. If you wrote this equation you will get most of the reit for the problem. What omes after is just algebra:.6 v 8 v With the numbers of the problem: v To simplify the problem notie that , so: v v v v It is easier to alulate β, where β is v/, so writing the equation as: v Solving for, we get: 7. ( ) So v = or.8x0 8 m/s

4 0) Length Contration An objet has a length of 8 m at rest, but it is moving at 60% the spee of light in the iretion of its length. How long oes it look? We fin gamma:. 5 v 0.6 L Length ontration: L o 8m m ) Momentum Calulate the momentum of an eletron when it has a spee of 0.98 in an aelerator use for aner therapy. The momentum of the eletron is given by. p mv 0.5MeV / (0.98).5MeV / 0.98 ) Energy What is the spee of an eletron whose kineti energy is.5 MeV? K m m v v K.5MeV m 0.5MeV 3) Aition of Veloities A roket is speeing away from the earth with a spee of A missile is fire from the roket at a spee of 0.45 with respet to the roket. Calulate the spee of the missile with respet to the earth. u = u' v u' v

5 Calulus Base Problems Intensity of Single Slit Light of wavelength 75 nm passes through a slit.5 μm wie an a single-slit iffration pattern is forme vertially on a sreen 3. m away. Fin the light intensity, I, 6 m above the entral maximum, expresse as a fration of the entral maximum s intensity, Io. We use Eq to alulate the intensity, where the angle is foun from the isplaement from the entral maximum (3. m) an the istane to the sreen. y 6m tan tan ( ).86 l 30m D sin (.5 x0 6 m) sin nm = ra = o I sin / sin(37.75 / ) I / ra / So the light intensity at 6 m is about 94.7% of the maximum intensity. Bragg Equation X-ray Diffration First orer Bragg iffration is observe at 8. o relative to the rystal surfae, with spaing between atoms of 0. nm. What angle will the seon orer be observe? What is the wavelength of the X-rays? Use Bragg Equation for X-ray iffration. m m sin sin where m = for seon orer. b) We nee to fin wavelength from the st orer. (0.nm) sin sin nm m m (0.978nm) a) sin sin = 70.4 o (0.nm) Doppler Shift A spaeship moving towar Earth at 0.70 transmits raio signals at 95.0 MHz. At what frequeny woul Earth reeivers be tune? f = fo v v = 5 MHz Note that the non-relativisiti frequeny woul be ompute as follows: f = fo ( + v/) = 95 MHz ( + 0.7/) = 6.5 MHz

Chapter 26 Lecture Notes

Chapter 26 Lecture Notes Chapter 26 Leture Notes Physis 2424 - Strauss Formulas: t = t0 1 v L = L0 1 v m = m0 1 v E = m 0 2 + KE = m 2 KE = m 2 -m 0 2 mv 0 p= mv = 1 v E 2 = p 2 2 + m 2 0 4 v + u u = 2 1 + vu There were two revolutions