Episode 315: The inverse square law

Transcription

1 Episode 315: The invese squae law This episode consides the ways in which the intensity o adiation deceases with distance om the souce. Summay Demonstation + discussion: adiation speading out, and an analogy. (0 minutes) Woked example: Thinking in popotions. (5 minutes) Student expeiment: Estimating the powe output o the Sun. (15 minutes) Student questions: Compaing lamps. (30 minutes) Demonstation + discussion: Radiation speading out and an analogy Set up thee simple demonstations: Bight lamp and phototansisto o othe light mete Micowave souce and detecto Gamma ay souce and Geige counte Show that the intensity o each type o adiation deceases with distance om the souce. (I students have aleady studied adioactivity, they may e awae o the invese squae law o gamma adiation.) Why does the intensity decease with distance? Ty to give two geneal easons. (Asoption and speading out.) Radiation speading out adially coves a igge and igge aea, popotional to, so its intensity deceases as 1/. It can help to think o a toast-utteing gun. The gun can utte a single slice o toast at a distance o 1 m. How can it utte ou slices simultaneously? (lace them in a aay at a distance o m.) How thick will the utte e? (1/4 o oiginal thickness.) Extend this to a 3 3 aay at 3 m, and so on. oint out that the intensity o adiation can e measued in watts pe squae mete (W m - ). Woked example: Thinking in popotions A coalt 60 souce gives a gamma dose ate o 160 μsv h -1 at 1.0 m away. At what distance will the dose ate e 40 μsv h -1? Answe: I the intensity has gone down y a acto o 4, the distance away must have douled to.0 m. O y k/d so I 1 /I d /d 1. 1

2 Student expeiment: Estimating the powe output o the Sun Students can make measuements to estimate the powe output o the Sun, making use o the invese squae law. Note that thee is a good oppotunity hee to discuss the validity o the answe otained. TA 315-1: Summe Sun ememeed Student questions: Compaing lamps Some calculations. TA 315-: Compaing intensities o lamps

3 TA 315-1: Summe Sun ememeed Measuing ightness, hoping to measue distance Compaing enegies incident on the ace allows an estimate o the distance o the Sun. You will need high-poweed lamp, pehaps 00 W (use a saety-patten atten lamp holde wied to plug diectly into a 13 A socket) ule patne Saety The second student is impotant, as one cheek will have to get quite close to the 00 W lamp. What to do Close you eyes, imagine lying on a each and ememe the summe Sun on you ace. How hot did it eel? Now ing you ace up close to a high-powe lamp take cae! A patne should watch you caeully, so that you do not touch the lamp. Aim to eel the same wamth that you ememe in the summe Sun. Recod the distance to the lamp and the powe o the lamp. ew cm 500 light seconds Sun 00 W powe? same osy glow same I lamp Sun ( lamp ) ( Sun ) 3

4 Can you use these data to suggest the powe output o the Sun? Rememe that the Sun is aout 500 light-seconds away. You have 1. Used the 1 / elationship to elate powe outputs. actical advice The incident powe pe squae mete is identical, and so application o the invese squae law will elate the powe outputs o the lamp and Sun to the distances o the two. A calculation can also show that the Sun's adiation at the Eath is o the ode 1 kw m. Saety The second student is impotant, as one cheek will have to get quite close to the 00 W lamp. Social and human context The powe output o the Sun might useully e compaed with the powe output o all human powe stations. Extenal eeence This activity is taken om Advancing hysics chapte 1, 50E 4

5 TA 315-: Compaing intensities o lamps Compaing ightness A low-powe lamp at close ange can oten appea as ight as a high-powe lamp much uthe away. Simila easoning is used to calculate the ightness o stas. Two ilament lamps Hee you compae two incandescent ilament lamps; one maked.5 V, 0.3 A and a second 100 W, 40 V. Assume that appoximately 0% o the powe dissipated y the lamps esults in visile photons eing emitted uniomly, and that oth ae eing un at nomal ightness. 1. Estimate the ightness o the 100 W lamp om 3 metes away, which is the luminous lux density in W m. Calculate how close you must e to the.5 V lamp to see it as eing the same lux density? Two loodlights This question is aout a 3 W icycle headlight and a 300 W exteio secuity loodlight. Both the loodlight and the headlight have appoximately the same shaped eam, a cone that coves appoximately 1 / 10 o a sphee. 3. Estimate the lux density o the icycle lamp om 0 metes away. 4. You pupil has a diamete o appoximately 0.01 m. How much light entes you eyeall pe second? 5. The loodlight looks just as ight as the icycle lamp. How a away is it? 5

6 actical advice All these questions involve use o the invese squae law, sameness o eam shape eing cucial in the questions aout the loodlights. Answes and woked solutions 1. 0 W as light, spead ove a sphee, o adius 3 m: 0 W 4 π 0 W 4 π 3 3 m 0.18 W m. owe as light.5 V x 0.3 A x W. This must spead ove a sphee, to give a lux density o 0.19 W m. 4π 4πI 4 π 0.18 W m 0.6 m W 3. 3 W as light, ocused onto 1 / 10 o sphee, o adius 0 m: 4 π 4 π 3 W ( 0 m) 6 mw m The pupil is catching light at 6 mw m : I A I π W m W. π The loodlight is 100 times moe poweul than a cycle light: m 6

7 π π I The loodlight is 10 times uthe away, 00 m. Extenal eeence This activity is taken om Advancing hysics chapte 1, 40S 7