swansont Posted July 25, 2015 Posted July 25, 2015 In the standard experiment, how much is the thickness of the slit and its relation to the photon's wavelength? There is no "standard" experiment. The fringe spacing will be z*lambda/d, where z is the distance to the screen, lambda is the wavelength of the light and d is the slit spacing. You can pick and choose values and do the experiment, as long as you are able to resolve the interference pattern. So you want z/d to be >>1, since the wavelength will be somewhere around half a micron for visible light, and you can't resolve that spacing with the naked eye — you might be able to resolve 50 micron spacing. (I think 50 is around the theoretical limit, that's around 500 lines/inch, or 20/mm)) http://farside.ph.utexas.edu/teaching/302l/lectures/node151.html https://en.wikipedia.org/wiki/Double-slit_experiment "For example, if two slits are separated by 0.5 mm (d), and are illuminated with a 0.6μm wavelength laser (λ), then at a distance of 1m (z), the spacing of the fringes will be 1.2 mm." So here z/d is ~2000 But you can buy gratings with 1 micron spacing and the screen won't have to be as far away.
michel123456 Posted July 25, 2015 Posted July 25, 2015 There is no "standard" experiment. The fringe spacing will be z*lambda/d, where z is the distance to the screen, lambda is the wavelength of the light and d is the slit spacing. You can pick and choose values and do the experiment, as long as you are able to resolve the interference pattern. So you want z/d to be >>1, since the wavelength will be somewhere around half a micron for visible light, and you can't resolve that spacing with the naked eye — you might be able to resolve 50 micron spacing. (I think 50 is around the theoretical limit, that's around 500 lines/inch, or 20/mm)) http://farside.ph.utexas.edu/teaching/302l/lectures/node151.html https://en.wikipedia.org/wiki/Double-slit_experiment "For example, if two slits are separated by 0.5 mm (d), and are illuminated with a 0.6μm wavelength laser (λ), then at a distance of 1m (z), the spacing of the fringes will be 1.2 mm." So here z/d is ~2000 But you can buy gratings with 1 micron spacing and the screen won't have to be as far away. Not the spacing. The thickness of the material used to make the slits.
swansont Posted July 25, 2015 Posted July 25, 2015 The material thickness is usually on order of the slit width, or less. I just made one with kitchen aluminum foil and an x-acto knife.
StringJunky Posted July 25, 2015 Posted July 25, 2015 The material thickness is usually on order of the slit width, or less Do they ensure the slit material is optically opaque? I presume they do but thought I'd ask.
michel123456 Posted July 25, 2015 Posted July 25, 2015 The material thickness is usually on order of the slit width, or less If i undertsand clearly that means the material thickness and the wavelength are of the same order of magnitude. It is like passing a baseball through a brick wall as thick as the diameter of the ball.
swansont Posted July 25, 2015 Posted July 25, 2015 If i undertsand clearly that means the material thickness and the wavelength are of the same order of magnitude. It is like passing a baseball through a brick wall as thick as the diameter of the ball. Standard aluminum foil is 16 microns, or 20x or so wavelengths of red light, which is what I used. Do they ensure the slit material is optically opaque? I presume they do but thought I'd ask. For transmission gratings, yes. You can also make phase gratings, which transmit but (as the name implies) varies the phase with a different index of refraction 2
michel123456 Posted July 25, 2015 Posted July 25, 2015 Standard aluminum foil is 16 microns, or 20x or so wavelengths of red light, which is what I used. For transmission gratings, yes. You can also make phase gratings, which transmit but (as the name implies) varies the phase with a different index of refraction Standard aluminum foil is 16 microns, or 20x or so wavelengths of red light, which is what I used. For transmission gratings, yes. You can also make phase gratings, which transmit but (as the name implies) varies the phase with a different index of refraction So, if the baseball is 73mm diameter, the wall with the slit within is 1,5 meter thick.
swansont Posted July 25, 2015 Posted July 25, 2015 So, if the baseball is 73mm diameter, the wall with the slit within is 1,5 meter thick. It doesn't have to be. It's partly a matter of structural integrity. It's hard to make a double slit by hand that's much thinner. Fabricated gratings are going to be thinner than what I made.
John Cuthber Posted July 25, 2015 Posted July 25, 2015 It is possible to repeat the experiment using microwaves with wavelengths of the order of a few cm and slits cut from foil. The "wall" can be thinner than the wavelength- the experiment still works. It's common to use material that's thicker than the wavelength of light- simply because a foil less than a two thousandth of a mm thick is difficult to work with.
swansont Posted July 26, 2015 Posted July 26, 2015 It is possible to repeat the experiment using microwaves with wavelengths of the order of a few cm and slits cut from foil. The "wall" can be thinner than the wavelength- the experiment still works. It's common to use material that's thicker than the wavelength of light- simply because a foil less than a two thousandth of a mm thick is difficult to work with. Or you can go much thicker, as with x-ray crystallography (or with electrons)
Lazarus Posted August 7, 2015 Author Posted August 7, 2015 Swansont said: Do you have evidence to back up your claim? Do you have a calculation that predicts the size of the interference pattern? If yes, please present them. Strange said: Or how about: you show us your calculations? ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Here is a simulation of Diffraction of Baseballs. The numbers are the number of times a baseball landed in that square. SINGLE EDGE 1232211221 233223133 2 11 32313 211222 35332111 1 33444452 1 1 1444233312 13222211221 12321 1353322322 254333133 2 12111 1132313 4223331 1 35333212 2 33444453 2 2 1655344312 24333211221 12321 2464422432 35433423412 1322211222213 1534344211 46443212 2 33443444 3 3 1655455312 36544423322 1331 2464422442 35333322221 2233222312 3 1534344211 46443212 2 3344233413 4 1655455312 34222322311 1331 2464422432 25544312322 22333333 2 2 1534233211 35333212 2 1433312332314 5434442 2 242222122 1 12321 1353322322 14433312322 22334342 1 1 1323122211 35332111 1 13222 2242414 3323331 1 221112122 1 12321 1232211221 14433211221 22334341 1323122211 23222111 1 12111 1142414 * 211222 221112122 1 12321 DOUBLE SLIT 12323344421221 2332464553333 2 11 11 323162313 2112431222 353356442211 1 334477964553 1 1 14443777353312 132235334421221 123222321 13534576542322 2543585663333 2 12112222424262313 42237533431 1 353367453412 2 334477974655 2 2 16554998464312 243356445421221 123222321 24646688742432 354369667543412 13223434433352213 15344976454211 464478563412 2 334467883747 3 3 16555998575312 365479777643322 13311331 24646688842442 353368555532221 22334456342612 3 15344976454211 464478563412 2 33445678363813 4 16555998575312 342257445432311 13311331 24646688742432 255468667532322 223355663535 2 2 15343866343211 353367453412 2 14334556635472314 54349854642 2 2422463442222 1 123222321 13534576542322 144347556532322 223365754443 1 1 13232545232211 353356442211 1 13223344626382414 33236633431 1 2211342332222 1 123222321 12323344421221 144346545421221 223365744341 13232545232211 232244332211 1 12112222525282414 * 2112431222 2211342332222 1 123222321 Y Single Edge Setup . . ........................................................................ . . . . b . u Floor . m-----------------------------------------------------------------X p . s . . . . . .......................................................................... . . Even with this crude simulation the diffraction patterns are evident. Also, this explains why the double splits have a stronger diffraction pattern than the Single Slit result. The overlapping patterns make the difference between the highs and lows greater. The mechanical set up is a Single Edge or a Double Slit, 39 feet above the floor with counters for each square foot of a 21 foot by 79 foot rectangle. The uneven edge (bumps) consists of 1 foot squares The Double slits are 3 feet wide, including the “bumps”. The space between the slits is 1 foot. The “bumps” are sloped down from horizontal at 3 different angles, 30, 39 and 51 degrees.. The “bumps” are bent down in the forward direction, then the sides are bent down with the horizontal size still 1 foot square.” Since the Double Slits are equivalent to 4 Single Edges all that is needed for the Double Slit version is to overlay one pattern with another shifted by the distance from one slit to the other which is 4 feet. One hundred baseballs were dropped on each “bump”, evenly spaced. The calculations The resulting angle of the bounce, A = s*(h^.5*f + 1)*(h*g + 1) The horizontal direction vector of the bounce = (1,(j-i)*0.5) The horizontal distance of the bounce = (39*cos(A)) / sin(A) Where A is the angle from horizontal of the bounce. s is the angle from horizontal of the bump before bending. (30, 39 or 51 degrees) f is the bend factor to bend the x direction of the bump down. (0.17) g is the bend factor to bend the sides of the bump down. (0.1) h is the distance along the x axis of the hit of the baseball on the bump. i is the distance along the y axis of the hit of the baseball on the bump. j is the location of the left center of the bump on the y axis. A better simulation program could produce a pattern to match light diffraction as closely as desired but the basic concepts are the same.
John Cuthber Posted August 7, 2015 Posted August 7, 2015 Swansont said: Do you have evidence to back up your claim? Do you have a calculation that predicts the size of the interference pattern? If yes, please present them. Strange said: Or how about: you show us your calculations? ------------------------------------------------------------------------------------------------------------------------------------------------------------------ Here is a simulation of Diffraction of Baseballs. The numbers are the number of times a baseball landed in that square. SINGLE EDGE 1232211221 233223133 2 11 32313 211222 35332111 1 33444452 1 1 1444233312 13222211221 12321 1353322322 254333133 2 12111 1132313 4223331 1 35333212 2 33444453 2 2 1655344312 24333211221 12321 2464422432 35433423412 1322211222213 1534344211 46443212 2 33443444 3 3 1655455312 36544423322 1331 2464422442 35333322221 2233222312 3 1534344211 46443212 2 3344233413 4 1655455312 34222322311 1331 2464422432 25544312322 22333333 2 2 1534233211 35333212 2 1433312332314 5434442 2 242222122 1 12321 1353322322 14433312322 22334342 1 1 1323122211 35332111 1 13222 2242414 3323331 1 221112122 1 12321 1232211221 14433211221 22334341 1323122211 23222111 1 12111 1142414 * 211222 221112122 1 12321 DOUBLE SLIT 12323344421221 2332464553333 2 11 11 323162313 2112431222 353356442211 1 334477964553 1 1 14443777353312 132235334421221 123222321 13534576542322 2543585663333 2 12112222424262313 42237533431 1 353367453412 2 334477974655 2 2 16554998464312 243356445421221 123222321 24646688742432 354369667543412 13223434433352213 15344976454211 464478563412 2 334467883747 3 3 16555998575312 365479777643322 13311331 24646688842442 353368555532221 22334456342612 3 15344976454211 464478563412 2 33445678363813 4 16555998575312 342257445432311 13311331 24646688742432 255468667532322 223355663535 2 2 15343866343211 353367453412 2 14334556635472314 54349854642 2 2422463442222 1 123222321 13534576542322 144347556532322 223365754443 1 1 13232545232211 353356442211 1 13223344626382414 33236633431 1 2211342332222 1 123222321 12323344421221 144346545421221 223365744341 13232545232211 232244332211 1 12112222525282414 * 2112431222 2211342332222 1 123222321 Y Single Edge Setup . . ........................................................................ . . . . b . u Floor . m-----------------------------------------------------------------X p . s . . . . . .......................................................................... . . Even with this crude simulation the diffraction patterns are evident. Also, this explains why the double splits have a stronger diffraction pattern than the Single Slit result. The overlapping patterns make the difference between the highs and lows greater. The mechanical set up is a Single Edge or a Double Slit, 39 feet above the floor with counters for each square foot of a 21 foot by 79 foot rectangle. The uneven edge (bumps) consists of 1 foot squares The Double slits are 3 feet wide, including the “bumps”. The space between the slits is 1 foot. The “bumps” are sloped down from horizontal at 3 different angles, 30, 39 and 51 degrees.. The “bumps” are bent down in the forward direction, then the sides are bent down with the horizontal size still 1 foot square.” Since the Double Slits are equivalent to 4 Single Edges all that is needed for the Double Slit version is to overlay one pattern with another shifted by the distance from one slit to the other which is 4 feet. One hundred baseballs were dropped on each “bump”, evenly spaced. The calculations The resulting angle of the bounce, A = s*(h^.5*f + 1)*(h*g + 1) The horizontal direction vector of the bounce = (1,(j-i)*0.5) The horizontal distance of the bounce = (39*cos(A)) / sin(A) Where A is the angle from horizontal of the bounce. s is the angle from horizontal of the bump before bending. (30, 39 or 51 degrees) f is the bend factor to bend the x direction of the bump down. (0.17) g is the bend factor to bend the sides of the bump down. (0.1) h is the distance along the x axis of the hit of the baseball on the bump. i is the distance along the y axis of the hit of the baseball on the bump. j is the location of the left center of the bump on the y axis. A better simulation program could produce a pattern to match light diffraction as closely as desired but the basic concepts are the same. So, nothing much to do with diffraction.
swansont Posted August 7, 2015 Posted August 7, 2015 Swansont said: Do you have evidence to back up your claim? Do you have a calculation that predicts the size of the interference pattern? If yes, please present them. Is there some reason that the formulas in the link I provided are not sufficient?
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