Young's double slit equation | Light waves | Physics | Khan Academy

Let's derive a formula that relates all the variables in Young's double slit experiment. Created by David SantoPietro.
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[@kenpachizaraki4184]

I had such a difficult time learning this in class for some reason. I really appreciate this. I don't know why but watching this made perfect sense to me. Maybe I'm just more of a visual learner. My instructor teaches concepts sometimes without illustrating. It makes it hard for me to visualize.

[@sabhighton]

kenpachi zaraki Can’t help but read this in Zaraki’s voice :)

[@mitchellrocky3847]

I dont mean to be offtopic but does someone know a tool to log back into an Instagram account..? I was stupid lost my login password. I appreciate any tips you can offer me

[@ShashiKumar-c3h2k]

A lot of people are struggling to understand why both lengths are equal at around 2:15 , here's why, The distance between both the slits (d) is very small and distance between the slits and screen is very very big, then by pythogorous theorem in that big triangle (X1)² = (X2)² + h²(h is the hypotenuse of the smaller triangle containing d and perpendicular in the bigger triangle) ,since h²

[@nurul5971]

thank u very much sir...i cant focused in my online class and my test is in three days and thankfully you save my lifeee

[@danpovey]

Arouynd 2:15, I notice a lot of people are pausing. I think he draws the right-angle symbol in the wrong place and it should be at the center, white line. Otherwise the argument doesn't seem to work. But I'm not a physicist and have not checked the argument all the way to the end.

[@Hunar1997]

I'm a physics student and i'm planning to get BIG marks in order to become a teacher, when i do that i will use the best method to teach my students, these and alot of other videos made it very clear how my method would be .. thanks i hope i will be as helpful as you guys :)

[@manzurulhaque4486]

Best of luck!

[@carpetman9191]

U a teacher yet?

[@Hunar1997]

@@carpetman9191 Almost, I became top of class.. now our names were presumably send to the government.. I'm waiting for the next season to come and see if I became a university teacher :) my dream might come true soon

[@carpetman9191]

@@Hunar1997 congradulations! I'm sure you will do great.

[@Hunar1997]

@@carpetman9191 Thanks :D

[@yorkregiontutoring]

The most important part of the video (just before and after 2:30) was quite poorly explained. Please consider making another video for students that demonstrates parallelism of lines, why the path lengths would be considered equal and why you placed the second theta where you had.

[@adityachandeliya6485]

awesome explaination :) !! Every faculty must teach like this one !!

[@ДенисМ-й2ж]

2:04 why the paths will be the same length? Aren't they cathetus and hypotenuse of right triangle, and can't be same length?

[@saharshpruthi]

Well sir i understand it as if the distance between the slits is very small as compared to the distance from the screen . say micro meters compared to a meter or so . For small angles the length becomes same .I hope i am right in my explanation.

[@joeford8035]

saharsh pruthi yes but for the interference pattern of light this approximation must be accurate enough for the wave length of light, roughly 550 nano meters, so im affraid i am also confused as to why this works. He did not explain this assumtion at all

[@juan041697]

Joe 1234 I'm also kinda confused about that, because if one angle is 90 an the 2 opossite sides are the same, that means the angles are the same and then we have a triangle with 2 90degree angles (not posible)

[@joeford8035]

yes well it doesnt hold to Pythagoras' theorem, however i believe that there is a convincing case that exists for the use of the small angle approximation here (which settles it) but it seems no one on youtube is willing to share it

[@siddhanttiwari5293]

Actually after that length as they are very close You could consider them parallel So only that small part is your delta x

[@muzzammilsajid]

1:58 I have a problem. How are those path lengths equal? I mean that's a right angled triangle in which hypotenuse is always greater, isn't it?

[@danpovey]

I suspect the right-angle is supposed to be on the white line, and it's supposed to be an isoceles, not right-angled triangle. I haven't watched it all though.

[@aaronge5195]

I hate to be that guy, but just in case any one else is confused, I gotta make a small correction. At 2:20, he says that the two sides highlighted in turquoise would be the same length, but that's impossible since one of the turquoise sides is the hypotenuse of a right triangle while the other side is not the hypotenuse.

[@Upgradezz]

It’s in the far limit it’s true

[@SA-sq7sf]

hats of to u guys u guys r just amazin' u make every thing so easy for us . love de khan academy

[@adishijha8365]

please explain ...why both of the angles are same

[@ArifWaqasofficial]

exactly what my question was!

[@qaboosmintaka5337]

I don't get it too. How did he equate the angle between the blue lines and the angle between the white lines?

[@alos.1198]

pause the video at 6:36 for observation in both triangles, there are 90° angles--------> (1) further, for constructive we know that : Δx =n λ so Δx (in red) and λ (in white, right beside the text "1st") can be considered to have a constant ratio Δx ----- = constant λ hence by triangle congruence, both of those angles are same

[@siriuss_7]

by triangle similarity

[@44USELESS44]

It's not drawn to scale, but in reality the two slits are really close together. This makes the rays from both slits essentially parallel and to the middle white line. If the angles are that small, both thetas are almost identical. you can try drawing the triangles yourself www.geogebra.org/geometry

[@JG12321]

I worked out a formula for Δx without using the sine approximation... I used the law of cosines a few times. If "d" is the distance between the centers of the slits, "L" is the perpendicular distance between the slit system and the back wall, and "y" is the height to the first order point, then: Δx = ( 2dy + d^2 ) / ( 2 * sqrt((y + d/2)^2 + L^2) ) The sine approximation (Δx = dsinθ) is good when "d" is very small compared to "y" (and to a lesser extent "L").

[@maizpalomeropuebla]

Hello. I just watch this video, is very good! thanks. But I want you check at 2:16. I have a question on this. If you take the right angle on where it is marked the two light blue paths marked are not equal. you most take the right angle on the white line so the both light blue paths have the same lenght... am I right?

[@demetriusjohnson5358]

i noticed it too bro! you're right, they screwed up here!

[@Ali_Massoud]

in the double slit experiment, the difference between distance between the slits and distance between each slit and the screen is significantly high, which makes the two lines approximately equal, but if you use the method in another application, where the distances are comparable, you can't make this approximation, as it would lead to a fatal error in calculations.

[@JimbobFaz]

Im confused at 2:10. Since if as he claims the 2 blue lengths are equal, then this forms an iscoles triangle and so the base angles are also equal. However, since the lower base angle is 90 degrees, this would also make the upper angle 90 degrees and you would not have a triangle but just a line. Consequently, the only thing that makes sense here is if this is just acttually an approximation. If this is the case then it would explain why he said the distance to the screen most be a lot further than the slit difference, as the approximation would get better then. If this is what he means here, why did he not clarify that for large comparable distance this is a good approximation.

[@thomasbradley3609]

Thanks, great video. 2:34 - Why are those two angles the same? Am I missing something obvious here?

[@jamesetheridge2199]

Thomas Bradley They are approximately the same if you assume the distance is large enough between the screen and the slits. Similarly the blue lines are only approximately equal.

[@hunterkim4891]

Thomas Bradley Okay so i think he made an errror or assumed that they were the same length due to the small difference of lengths, but as far as I know, the orange line should be perpendicular to the white line that makes theta, not the blue line.

[@siriuss_7]

By triangle similarity

[@ivar1476]

+Tee Ponsukcharoen could you please explain

[@TheAnonymousUchiha]

They are similar triangles

[@RealEverythingComputers]

Explained way better than any textbook! Thanks so much

[@fadhilfatih6134]

2:37 how did you know that the angles are the same?

[@dishachakraborty2184]

Now this is a really good explanation for someone who knows nothing about Young's experiment and has to get it prepared for tomorrow's exam !!!👍

[@islampeace5518]

how are the angles the same at 2:34, don't say that the distance between the screen and the source is much larger than the distance between the slits... I know that but how does that allow you to assume that the angles are the same

[@44USELESS44]

www.geogebra.org/geometry. Try drawing the same triangles here, because the distance between the two slits are sooo small(drawing a reallly tiny triangle). you will see that the theta in the orange triangle is almost equal to the theta in the white triangle

[@AVirk]

How did he equate the Q angles in the two triangles

[@unique1o1-g5h]

1:56? why is that line drawn and how is it perpendicular and how is deltaX's length below that line. How is that for sure?? looks like an assumption . can someone explain to me

[@khyoman]

+Yunik Maharjan Yes, It is an assumption. We can use this assumption because this normal to deltax has a very smal size, and we know that as the normal approaches zero, the two "paths" will equal.

[@ShamimaAhmed-m5s]

can anyone explain in 2:17 why that 2 lentgh will be equal if it is right angle? and why the angle is the same is theta?

[@vhuhwavhosingo8294]

Wow what a good teaching 👏

[@ashikasaiunnikrishnan]

Thank you😁

[@dibyaroopbose]

it made my concepts crystal clear....

[@raunaksinghdhanjal4168]

Best teacher on KZbin

[@AFKabi]

You can also replace Sin for y/H where y is position on the screen from the center of it and H (Hypotenuse) is distance to the screen from the center of the origin. If you move it around (and do some approximations Like making H = Distance from center to center) you can get the positions on the screen based on the wavelength, d and D. y = (D/d) n Lambda

[@KakarotM99]

I know this formula is correct but Y/D is tan theta

[@lpenney49]

Kabir Manrai tan theta is approximated to be equal to sin theta when the distance between the slits (d) is very small compared to the distance from the slits to the screen.

[@KakarotM99]

lpenney49 oh yeah, thanks

[@Teresa-nn5xq]

How can it be possible for a isosceles triangle with two right angles?

[@A.M.Atamna]

How can the hypotenuse in a right triangle from the path lengths be equal to the opposite??

[@aizasaed170]

Finally got it👐 thank u💜

[@taqwatoqee5016]

thank you soo much .. I'm in my senior year in high school and this year will control what college I will enter and that's after 3 months hhhh .. you helped alot thank you soo much again ♥

[@GameOnBeast]

Wow amazing!!! You explain wonderfully

[@eugenechoi9146]

sorry for this silly question, but why do we number "m" the way we do, such as 1, 1.5, 2, 2.5, etc? What does the number mean? Is it similar to how electrons are quantized?

[@Jindsing]

is it true the output on the wall will change depending if the waves are being observed or not? IE: if the output is not being observed it would appear as if there was only 2 intense points with equal intensity?

[@jakeaustria5445]

You are wrong at drawing where the right angle is supposed to be in 2:00. It is not necessarily equal with how you presented it. The right angle is supposed to lie on the white line above the central line. You did not show your "basic trigonometry" in 2:14 or so. That's maybe why the errors stockpiled. Please reupdate your video.

[@gen-zstars8813]

Thanks 😍

[@GilbértoFeliú]

Can someone please explain why the angle opposite to the Δx side in the right triangle is equal to theta? Theta originally being the angle between the line cutting through the central maximum and the line going to the int. fringe.

[@fadhilfatih6134]

It's been 3 years, did you already find out why?

[@haaani__]

It's been 5 years did u get??

[@宮崎凛]

Thanks for uploading that video! It's really helpful: )

[@DominikJuzeHaus]

3:33 those 2 blue sides of the right angle triangle definitely do not have the same lenght, or am I just tripping?

[@itsmeilay]

Thank you for this great explanation this helped me so much with school i am from Turkey by the way

[@Uygʻun-q2c]

thanks brother

[@sanjuansteve]

How are double slit test results changed when using polarized light either aligned with the slits or perpendicular to them, as well as with helical? Thx

[@Hemanthdev10]

Amazing!

[@alesv77]

2:00 he says "if this is right angle right here," then the two purple paths are equal. Not at all! They are a cathetus and a hypotenuse of a triangle.

[@TheLogMan123]

where L >>>>>>>> d they are very close to equal.

[@anjalidutta8471]

For very very very very small thetas , they are assumed to be almost equal

[@Hemanthdev10]

AMAZING!

[@florenceting9824]

thanks for teaching well through online video. :)

[@syedsaadqainhaider2456]

what is the effect of light intensity ion the fringe spacing??

[@muhammadanas459]

in 6:18, how to measure the angle???

[@tylerlitch3992]

What screen recording software do you use? I would like to know a good one that allows me to pause recording.

[@symphonyofsolidarity]

2:25 opposite side is equal to hypotenuse???? What

[@elliottwilliams185]

very well explained thank you

[@blessos]

Still not convinced by the hand wavey justification given in all explanations as to why it's ok to assume the two paths minus the path difference form a right triangle. They don't they obviously form an isosceles triangle as the whole point is that they are the same length!

[@harshalpatil6098]

Very much detailed and nice explanation 👍🏻

[@dhruvpanchal11]

Nice explanation thank you

[@noname-sg6qx]

Isn't the equation for this a=D(lambda)/d, where a is the fringe spacing and D is the distance from the screen to slit and d the distance between the 2 slits?

[@jeffc7971]

Thank you!

[@jesulebo7680]

Awsome video! Keep making more!

[@chll-hub7642]

what grade or stufy level yall in, rn 2021

[@muazzam1990]

Good explanation I love you...

[@mohamadosman5344]

just saved my life! thank you

[@wasifjalal6965]

what is m for?

[@rohitsanjay1]

maximum or minimum. It depends on what value they hold at a certain location on the screen. If it's a half-number, its a minimum (dark spot) and if its a whole number, then its a max (bright spot)

[@tomriddle9740]

How is sin equal to base /hypotenuse ?

[@JonasUllenius]

Is there a possibility of making a real photon experiment where there are not enough photons to make a solid line? Are there ways of seeing photons through a prism and make the different wavelength go trough different slits?

[@trojan9838]

Why do we take the paths of the waves to be parallel? That's the only way the two thetas are equal.

[@knucklesamidge]

THANK YOU SO MUCH I LOVE YOU

[@dreamer9071]

How can the length be same..There are two right angles,If u make one right angle

[@adibreshad8837]

I didnt understand why the two angles are the same and what it has to do with the second plane being far away . someone please help .

[@muhamadmirzaazribindzulzal5447]

Can someone please help me, I don't understand why when a question asks for the third order minima we take m=2, but when it asks for third order maxima we take m=3? Is the nth order not the same as order number=n for destructive?

[@VG__]

5:55 summary.

[@siriuss_7]

someone explain me the relation of lambda on screen ...like how the crust and trough meet the screen

[@raspberry765]

why are those two angles the same?

[@vietto271]

Wow i didn’t think about using angle to measure wavelength We are taught to use this fomula: Δx = λD/a D is the distance between the slits and the screen in meter a is the distance between two slits in millimeter Δx is measured in centimeter And i should have the wavelength in micrometer Thanks for the knowledge

[@codingbarber6674]

I thought the formula was wave length = (distance between slits * distance between 2 bright fringes) / Distance from laser to board

[@anjalidutta8471]

how have you taken the 2 path lengths to be equal? then the other side of the 90° would also be a 90° and this would have to be equal to the opposite angle sonce the two path lengths are equal...then it would not form a ∆ at all

[@abhinavgyawali3253]

Exactly. That's the same thing that I've been thinking. It doesn't really make sense.

[@sanjuansteve]

I’ve been saying since 2013 that it seems extremely obvious that all electrons and photons are in orbit with a dark matter particle. Based on Fermilab and other recent findings, I now think electrons are made of an electron neutrino entangled in orbit with a dark matter muon neutrino, explaining their erratic orbits around nuclei and explaining superposition and uncertainty. I think photons are a pair of electrons entangled in orbit together in apparent an axial or helical polarizable wave-like movement depending on the direction of their rotation as they travel. This explains the double slit experiment for example and the speed of the rotation explains electromagnetic wavelengths (and visible colors, etc). What do you think of this Mudfossil University video?: ‘’Light Duality Solved and Seen’’, Sep 29, 2022

[@abdullahatallah9759]

AmaZing

[@mohamedgamal7600]

Why are angles the same ?

[@tabe8850]

Because they both watch MSNBC.

[@shakirayoubmir7270]

Super

[@michael-jayasuriya]

what if the wavelengths are different?

[@wiremucurtis4865]

Michael Jayasuriya Then you wont get regual fringes, if any at all. They wont interfere properly

[@giveherheadnotheadaches]

thanks, lightning McQueen.

[@alos.1198]

i guess the angle is gonna be very small....so can't we just assume sin Θ = Θ (in radians)

[@birdman4274]

How the hell did they make the holes so small and so close back then?

[@bogdanRandom]

the remainder of the pads form a straight angle triangle. They cannot be equal, based on Pitagora theorem. Why did you say they are equal? in this drawing delta x is not the pad difference! Is larger than the pads difference

[@VG__]

1:58

[@sharmass3756]

super

[@annajuliaschwarz490]

that angle theta was so random what happened there!

[@aayushphadte]

*Green Green Green Green Green!*

[@楚阿克]

My optics teacher has a so special dialect that I cant't understand him.

[@evetoylekatiliyorjm]

is sin theta changeable or constant here?

[@sl2357]

umm... slit spacing are small, the screen is far away... small... far away...

[@elizabethturnbull3524]

i love you

[@ajaypriyadharshan9484]

Is ø pronounced theta or tita

[@sahilyadav2883]

Ajay Priyadharshan its called as phi

[@AnuragsharanTG]

Phi

[@Hidden8009]

The cursor really makes it too difficult for me to understand about what he's teaching..can barely see it

[@larrynmcmahan9536]

Lies, lies, all lies. You must make the the cross line at right angles to the *centerline*. This make the difference in distances tan θ, not sin θ. You then have to approximate tan θ as sin θ for small angles. You get your answer, but it is only an estimate based on the closeness of tan and sin for small angles.

[@shujiancao4599]

This formula is a disgrace, you can absolutely get the answer without assuming the hypotenuse and the adjacent being the same. I don't get it, this is physics, how can we just assume something like this. In my IB textbooks, they don't even explain how to get the formula, and this video is very ambiguous concerning the assumptions there. I mean, here's the thing. You can argue that the difference between the hypotenuse and the adjacent is small, but we are taking wavelength into consideration here, which is in the nanometer level, the error would be big compared to the wavelength.

[@sccm100]

I hate physics