Physics Optics Homework Assignment #1. Problem 1-2 : Problem 1-3 : Chapter 1: #2, 3,10,12,13,15,16,17

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1 Physis Optis Homework Assignment #1 Chapter 1: #, 3,10,1,13,15,16,17 Problem 1 - : ü The threshold sensitivity of the human eye is about 100 photons per seond. The eye is most sensitive at a wavelength of around 550 nm. For this wavelength, determine the threshold in Watts of power. Solution : Eah photon has an energy of h.the threshold power l is the rate at whih the photons arrive times the energy per photon. l = 550. * 10-9 ; H* m *L energyperphoton = h * l ; Print@"Threshold power for the eye = ", energyperphoton * 100, " Watts"D Threshold power for the eye = µ Watts Problem 1-3 : ü What is the energy, in eletron volts, of light photons at the ends of the visible spetrum? Solution : 1 eletron volt is 1.60 x Joule. Use the formula h l, and onvert to eletron volts. wavelengths = 8770., 380.<; H* nm, Hfrom Figure 1-1 in textl *L ev = 1.60 * ; H* JoulesêeV *L energyperphoton = h * ; wavelengths * 10-9 Print@"Photon energies = ", energyperphoton ê ev, " eletron Volts"D Photon energies = , < eletron Volts

2 Homework_Ch_01.nb Problem 1-10 : ü Solar radiation is inident at the earth's surfae at an average of 1000 W/m on a surfae normal to the rays. For a mean wavelength of 550 nm, alulate the number of photons falling on 1 m of the surfae eah seond. solarirradiane = 1000.; H* Wattsëm *L l = 550. * 10-9 ; H* m *L energyperphoton = h * l ; numberofphotons = solarirradiane energyperphoton *.01 ;H* per square entimeter *L 1 Print@"Number of photons per square m = ", numberofphotonsd Number of photons per square m =.7687 µ Problem 1-1 : ü Calulate the band of frequenies of eletromagneti radiation apable of produing a visual sensation in the normal eye? Solution: Use n = /l to onvert 380 nm and 670 nm to frequenies. wavelengths = 8770., 380.<; H* nm, Hfrom Figure 1-1 in textl *L frequenies = ; H* Hz *L -9 wavelengths * 10 Print@"Frequeny range of visible light = ", frequenies, " Hz"D Frequeny range of visible light = µ 10 14, µ = Hz Problem 1-13 : ü What is the length of a half-wave dipole antenna designed to broadast FM radio waves at 100 MHz? Solution: A half-wave dipole antenna has a length of one-half of the wavelength for whih it is designed. Find the wavelength of a 100 MHz eletromagneti wave and divide by two. frequeny = 100 * 10 6 ; H* Hz *L wavelength = frequeny ; Print@"wavelength = ", wavelength, " m"d Print@"Antenna length of a half-wave dipole = ", wavelength ê. " m"d wavelength =.998 m Antenna length of a half-wave dipole = m

3 Homework_Ch_01.nb 3 Problem 1-15 : ü A soprano's voie is sent by radio waves to a listener in a ity 90 km away. ü a) How long does it take for the soprano's voie to reah the listener? frequeny = 100 * 10 6 ; H* Hz - doesn't matter for this problem *L emtime = ; Print@"Time for radio wave = ", emtime * , " miroseonds"d Time for radio wave = 300. miroseonds ü b) In the same time interval, how far from the soprano has the sound wave in the auditorium traveled? Take the speed of sound to be 340 m/s. v = 340.; H* mês *L sounddistane = v * emtime; Print@"Distane travelled by sound wave = ", sounddistane, " m"d Distane travelled by sound wave = m Problem 1-16 : ü A small, monohromati light soure, radiating at 500 nm, is rated at 500 W. Solutions: a) Radiant Intensity = b) Radiant Exitane = ) Irradiane = Solid Angle Soure Area Area at Sreen d) Radiant Flux = (Irradiane) (Surfae Area of Hole) ü a) Radiant Intensity: If the soure radiates uniformly in all diretions, determine its radiant intensity. l = 5.00 * 10-9 ; H* not needed for this problem, exept to show it is visible light *L radiant = 500.; H* Watts *L radiantintensity = radiant ê H4 pl; H* Watts per sr *L Print@"Radiant Intensity = ", radiantintensity, " Wattsêsr"D Radiant Intensity = Wattsêsr ü b) Radiant Exitane: If the surfae area of the soure is 5 m, determine the radiant exitane. emittersurfaearea = 5.0 * 10-4 ; H* square meters *L radiantexitane = radiant ê emittersurfaearea; PrintA"Radiant Exitane = ", radiantexitane, " Wattsêm "E Radiant Exitane = 1. µ 10 6 Wattsêm

4 4 Homework_Ch_01.nb ü ) Irradiane: What is the irradiane on a sreen situated m from the soure, with its surfae normal to the radiant flux? r =.; H* meters *L Irradiane = radiant ë I4 p r M; PrintA"Irradiane = ", Irradiane, " Wattsêm "E Irradiane = Wattsêm ü d) Radiant Flux: If the reeiving sreen ontains a hole with a diameter of 5 m, how muh radiant flux gets through? holearea = p.05 radiantflux = Irradiane * holearea; Print@"Radiant Flux through the hole = ", radiantflux, " Watts"D Radiant Flux through the hole = Watts Problem 1-17 : ü A 1.5 mw helium-neon laser delivers a spot of light 5 mm in diameter aross a room 15 m wide. The beam radiates from a small irular area of diamter 0.5 mm at the output mirror of the laser. Assume that the beam irradiane is onstant aross the diverging beam. Solutions: a) Beam Divergene Angle = Effetive radius = b) Solid Angle = ) Irradiane = d) Radiane = Change in Beam Diameter Distane to Wall Ar Length = Radius Final Beam Diameter = radius if light had ome from a point, spreading to a 5 mm diameter spot. Beam Divergene Angle Final Beam Area Effetive Radiuss Reeived Beam Area HSolid AngleL*HBeam AreaL ü a) Beam Divergene: What is the beam divergene angle of this laser? In[36]:= divergeneangle =.0045 ê 15; H* radians *L Print@"Divergene angle = ", divergeneangle * 1000, " milliradians"d Print@"Divergene angle = ", divergeneangle * 180 ê p, " "D Divergene angle = 0.3 milliradians Divergene angle = ü b) Solid Angle: Into what solid angle is the laser sending its beam? In[0]:= spotarea = p.005 ; H* square meters *L solidangle = spotarea 15 ; H* AëR, in steradians *L Print@"Solid Angle of Beam = ", solidangle, " steradians"d Solid Angle of Beam = µ 10-8 steradians

5 Homework_Ch_01.nb 5 ü ) Irradiane: What is the irradiane at the spot on the wall 15 m from the laser? In[3]:= radiant = 1.5 * 10-3 ; H* Watts *L Irradiane = radiant ê spotarea; PrintA"Irradiane = ", Irradiane, " Wattsêm "E Irradiane = Wattsêm ü d) Radiane: What is the radiane of the laser? In[38]:= exitarea = p.0005 ; H* square meters *L radiantintensity = radiant ê solidangle; radiane = radiantintensity ê exitarea; Print@"Radiant Intensity = ", radiantintensity, " Wattsêsr"D PrintA"Radiane = ", radiane, " Wattsêsr-m "E Radiant Intensity = Wattsêsr Radiane = µ Wattsêsr-m