Massachusetts Institute of Technology Physics 8 03 Fall 2004 Problem Set 11 There is no due date for this problem set but the topics covered here including the Take Home experiment are all part of the Final Exam I will post the solutions on Friday December 10 Reading Assignment Beke Barrett pages 559 584 Problem 11 1 Take home experiment 9 Transmission grating The text mentions a mini maglite to do some of the experiments The maglite however was not put in your 8 03 kit this term I suggest that you use a ashlight instead Use some black paper with a small hole in it to reduce the size of the light I also recommend that you use your color lters when doing some of the experiments with your grating even though that is not suggested in the text Using the lters will give you some extra insight That s why I added them to your optics kit envelope The optics kit is yours to KEEP and to ENJOY I always carry a grating and a linear polarizer on me The polarizer is great to look at the blue sky at rainbows and more and the grating is priceless to look at various bright lights mercury lamps Choose a light that is FAR AWAY e g across the river to minimize the angular dimension of the light this will give you the best spectral resolution possible as demonstrated in lectures Please return the 8 03 experiment kits on Monday 12 6 3pm 6pm or on Tue 12 7 11am 1pm Problem 11 2 Think big The criterion for Fraunhofer di raction is z 2D2 Beke Barrett eq 8 71 a What is the meaning of z D and The rst zero in the case of single slit Fraunhofer di raction is found when sin Barrett page 584 D b Use this result to derive in a single line that z should be larger than a few times a very easy way to appreciate the Fraunhofer criterion Beke D2 This is Gedanken Experiment Suppose we want to observe Fraunhofer s single slit di raction from a star 10 light years away from us As far as the above condition is concerned we could make the slit 1 about 12 meters wide without losing our Fraunhofer di raction pattern that we want to observe on a screen Take 500 nm as the wavelength c What should the approximate minimum distance be between the slit and our observation screen photographic plate d How wide would the central bright maximum approximately be on our screen Try to predict rst then calculate Now leave the screen and slit in place but narrow down the slit width to 2 meters e First try to predict then calculate the approximate width of the central bright maximum on the screen Don t be too hasty with your prediction f What would be the approximate width of our central bright maximum due to di raction if we made the slit 96 meters wide without changing the distance between the gap on Earth and the screen on the Moon g List your reasons why the above gedanken experiment would never give satisfying results Problem 11 3 Beke Barrett 8 7 amended Angular resolution Two bright lights are 1 ft apart and 10 miles away They are observed by a telescope the lens of which has a diameter of 5 cm A slit is placed in front of the lens and oriented so that its width is parallel to the line that connects the two lights The slit width is variable and it is narrowed until the two lights are just barely resolved Find its width assuming the e ective wavelength to be 6000 A Problem 11 4 Pinhole camera Do problem 8 8 from Bekefi and Barrett Electromagnetic Vibrations Waves and Radiation Cambridge MA The MIT Press September 15 1977 ISBN 0262520478 A pinhole camera for visible light is made from a cubical box length of one side L by drilling a small circular aperture diameter d in one side and using the opposite inside wall as the screen where the lm is placed Approximately what value of d will provide the sharpest image on the lm Hint Calculate the full size of the geometrical plus di raction image of a distant source Problem 11 5 Double slit interference Do problem 8 9 from Bekefi and Barrett Electromagnetic Vibrations Waves and Radiation Cambridge MA The MIT Press September 15 1977 ISBN 0262520478 A plane electromagnetic wave of wavelength 0 is incident on two long narrow slits each having width 2a and separated by a distance 2b with b a One of the slits is covered by a thin dielectric plate of thickness d and dielectric coe cient with d chosen so that 1 d 0 5 2 The interference pattern due to the slits is observed in a plane a distance L from the slits where L is large enough so that the far eld approximations may be used that is the pattern depends only on the angle from the normal to the slits as shown a Consider e ects due to interference only What is the condition for a maximum in the pattern Sketch the interference pattern 2 b Now include e ects due to both interference and di raction How is the intensity distribution modi ed from that obtained in a Let b a 10 sketch the resulting interference di raction pattern Assume that all angles involved are small enough so that cos 1 and hence that the optical path through the dielectric is independent of angle 3