Wishing you a very Happy Guru-Purnima Professor, Today is an auspicious day in India where we show respect to our Gurus(Teachers, Mentors, Coach) by wishing them. Thank you so much for your lectures, and continuous support to the students community.
Using the formula nλ =dsinθ (Eq [1]) for n=1, and knowing that d=0.24x10-9 θ=26.2° it is trivial, and in fact more straightforward to get the wavelength of the x-rays first λ=(0.24x10-9) sin(26.2°)= 1.06x10-10 ≈ 1 angtrom and then plug n=2 in Eq [2] and solve for theta to get the second order maxima, i.e. θ= arcsin(2λ/d) = 62° Lecture 34 of 8.02 uses Eq [1] for diffraction gratings, here we are using it for a crystal. In the former case we are in the physics’s world of Optics, in the latter we are dealing with Solid State Physics. However, the formula is the same. The reason: the crystal acts like a grating being the groves the space in-between the atoms. That’s why we call it Bragg DIFRACCTION Nonetheless, I think it is important to emphasize that the geometric derivation that Walter Lewin does of Eq [1] in the Lecture prior to 34, that is Lec 33 (minutes 18-20) is done for a diffraction grating, the geometry for Bragg diffraction where the light source does not strike the layers of atoms perpendicularly is different. Fortunately the result is the same and the formula is valid
To solve these problems, we can use Bragg's Law, which is given by: \[ n\lambda = 2d\sin\theta \] where: - \( n \) is the order of the diffraction, - \( \lambda \) is the wavelength of the X-rays, - \( d \) is the spacing between the crystal planes, - \( \theta \) is the angle of diffraction. Given: - First-order Bragg diffraction (\( n = 1 \)) is observed at \( \theta_1 = 25.2^\circ \), - Spacing between the planes, \( d = 0.24 \) nm. ### Part (a): Angle for the second order For the second-order diffraction (\( n = 2 \)), we need to find \( \theta_2 \). First, we find the wavelength using the first-order condition: \[ \lambda = \frac{2d\sin\theta_1}{n} \] \[ \lambda = \frac{2 \times 0.24 \times \sin(25.2^\circ)}{1} \] Calculating the sine value: \[ \sin(25.2^\circ) \approx 0.426 \] Thus, \[ \lambda \approx 2 \times 0.24 \times 0.426 \approx 0.20448 \text{ nm} \] Now, for the second order (\( n = 2 \)): \[ 2\lambda = 2d\sin\theta_2 \] \[ \sin\theta_2 = \frac{2\lambda}{2d} \] \[ \sin\theta_2 = \frac{\lambda}{d} \] \[ \sin\theta_2 = \frac{0.20448}{0.24} \approx 0.852 \] Thus, \[ \theta_2 = \sin^{-1}(0.852) \approx 58.4^\circ \] ### Part (b): Wavelength of X-rays From the first-order calculation: \[ \lambda \approx 0.20448 \text{ nm} \] Therefore: - The second order will be observed at approximately \( 58.4^\circ \). - The wavelength of the X-rays is approximately \( 0.20448 \) nm. Yunus ghausi, P.E, T.E, PPM, MS, Yunus.ghausi@outlook.com
Q-1) The answer can be easily found from the Bragg Diffraction Formula given by: n*lambda = 2d*sin(theta) In this case, because of the first order diffraction is happening at n=1, putting the number gives us: 1*lambda = 2*0,24 nm*sin(26,2°) lambda=0,211 nm Q-2) In this case, the second order diffraction is asked and it means that n=2 2*0,211 nm = 2* 0,24 nm *sin(theta) theta = arcsin(0,211/0,24) = 61,54° I hope I didn't do a mistake😅 Sir, there isn't anyone who can even be close to you in teaching and arouse curiosity abot physics and you are the best one in this field!! When 4,5 years ago, I was in trouble because no one could teach us physics good and in an "intuitively pleasing" manner. And I couldn't find answers tı my questions. Then I found you and my life is entirely changed by your 8.02 lectures. I decided to study electrical engineering, which is a very nonintuitive area. Because you made me understand the electromagnetism even through it is a very non intuitive and a hard field. You did a "magic touch" to me, and I believed you effected a lot of students like me in a positive way all around the world. I think that UN should give you a kind of prize!! I apologize on my part to not watch all of your scientific problem solving videos, I will try to watch them more often. You should definetely continue to do these videos!! WE ARE ALL YOUR STUDENTS SIR. WE ARE WALKING IN THE PATH THAT YOU OPENED AND TO THE GOAL THAT YOU SHOWED. "Gratings" (😂) from Türkiye 🇹🇷
Bragg’s law: n* λ = 2d * sin θ. First order n= 1 λ = 2d * sin θ = 2 * 0,24nm * sin (26.2) = 0,21 nm (answer to b) Second order n = 2 Sin θ = (2λ/2d) = 0,42/0,48 = 0,875 θ = arcsin(0,875) = 61 degrees (answer to a)
Using Bragg's Law nλ=2dsin(θ) The second-order diffraction will be observed at an angle of approximately 62.01 degrees, The wavelength of the X-rays is approximately 0.212 nm.
Oh boy, I'm making a mess of this compared to other's answers. Is theta here the complement of the angle in the lecture? Should the second order angle then be smaller than the first order as defined here? Is the spacing here perpendicular to the spacing in the optical grating in the lecture?
I like that you are trying to understand where Bragg's Law comes from. Ask yourself how does a vertical row of atoms compare to a vertical row of slits. Think Huygens sources. Then think about the condition needed for constructive interference. WL covers this and also in his 8.03 Lect 21.
I looked up the diagram online and I see that my path diagram was wrong somehow. Now I get lambda = 2dsin(theta) = 0.2119... nm and theta2 = arcsin(lambda/d) = 62.0078... degrees Still puzzling why my diagram was wrong.
Hello sir Hope you are doing well How does image formation happen in water i mean i have seen the image of house which looks like its inverted in water and position of it seems just down the actual house Is it same as concave mirrors Does water also have focus and centre of curvature etc is the image forming on the centre of curvature I am confused , is there any connection btw concave mirrors and this image formation in water I'm sorry I'm not good at explaining my questions But i hope you got it
@@lecturesbywalterlewin.they9259 i went through few websites but I am not able to imagine it How reflection? Well , I haven't even properly understood reflection , I just know it's bouncing back of light...but what does it actually mean ,how is it forming images I can't find the right source But thank you I'll Try to find out
It's basically just a nature of geometry.If you cast two parallel rays,one ray from the top of a house and one ray from the bottom.Then when they get reflected,the bottom ray always get higher than the top ray,it's just geometry.Why parallel rays?All points in space emit so many arbitrary rays but only parallel rays got focus in at the focal plane equal a distance of focal length(infinity focus means all far objects have more absolute parallel rays than closer objects).And you can imagine like this: each point in infinity would have different poisitions in x and y on the focal plane but they share the same z(focal length).The reason you see the house image from the water reflection is your eyes are convex lenses,without the biological lens you can't see the image being formed.
Sir, I am Soumyadip Maity, an engineering student from India. In 8.02 spring 2002 Electricity and Magnetism, you told us(your TH-cam students) to study a book by D. C Giancoli. But I can't find the eBook of this book recommended by you. Sir, I will be grateful to you if you give me the link to the book.
8.01 Physics Hans C. Ohanian Physics Volume 1 2nd edition W.W. Norton & Company ISBN 0-393-95748-9 8.02 Physics for Scientists & Engineers by Douglas C. Giancoli. Prentice Hall Third Edition ISBN 0-13-021517-18 8.03 Vibrations and Waves by Anthony French CRC Press ISBN 9780748744473 8.03 Electromagnetic Vibrations, Waves and Radiation by Bekefi and Barrett. The MIT Press ISBN 0-262-52047-8 ---
Vraag van mijn dochter in het kader van dierenartsopleiding mbt rontgenbuizen : " als je een elektronenversnelling onder een spanning van 100 volt zet dan hebben die elektronen toch ook 100 elektronenvolt??" Weet U het ?
@@lecturesbywalterlewin.they9259 ha... dank van mijn dochter. Heet trouwens ook Emma .... ze moet nog 1.5 jaar in utrecht.. 6 jaar opleiding en ze moest onderweg nog een jaar wachten vanwege plaatsgebrek ....
Wishing you a very Happy Guru-Purnima Professor, Today is an auspicious day in India where we show respect to our Gurus(Teachers, Mentors, Coach) by wishing them. Thank you so much for your lectures, and continuous support to the students community.
Fun fact:- you have 71 Subscribers and 71 comments on this channel 😅
@@Dakshmaths11 Oh i see !
Salute to this man for still delivering knowledge even at this age.
Age no matters...... .
Sir you are the best teacher of physics in the world 🌍
Using the formula
nλ =dsinθ (Eq [1])
for n=1, and knowing that
d=0.24x10-9
θ=26.2°
it is trivial, and in fact more straightforward to get the wavelength of the x-rays first
λ=(0.24x10-9) sin(26.2°)= 1.06x10-10 ≈ 1 angtrom
and then plug n=2 in Eq [2] and solve for theta to get the second order maxima, i.e.
θ= arcsin(2λ/d) = 62°
Lecture 34 of 8.02 uses Eq [1] for diffraction gratings, here we are using it for a crystal. In the former case we are in the physics’s world of Optics, in the latter we are dealing with Solid State Physics. However, the formula is the same. The reason: the crystal acts like a grating being the groves the space in-between the atoms. That’s why we call it Bragg DIFRACCTION
Nonetheless, I think it is important to emphasize that the geometric derivation that Walter Lewin does of Eq [1] in the Lecture prior to 34, that is Lec 33 (minutes 18-20) is done for a diffraction grating, the geometry for Bragg diffraction where the light source does not strike the layers of atoms perpendicularly is different. Fortunately the result is the same and the formula is valid
To solve these problems, we can use Bragg's Law, which is given by:
\[ n\lambda = 2d\sin\theta \]
where:
- \( n \) is the order of the diffraction,
- \( \lambda \) is the wavelength of the X-rays,
- \( d \) is the spacing between the crystal planes,
- \( \theta \) is the angle of diffraction.
Given:
- First-order Bragg diffraction (\( n = 1 \)) is observed at \( \theta_1 = 25.2^\circ \),
- Spacing between the planes, \( d = 0.24 \) nm.
### Part (a): Angle for the second order
For the second-order diffraction (\( n = 2 \)), we need to find \( \theta_2 \).
First, we find the wavelength using the first-order condition:
\[ \lambda = \frac{2d\sin\theta_1}{n} \]
\[ \lambda = \frac{2 \times 0.24 \times \sin(25.2^\circ)}{1} \]
Calculating the sine value:
\[ \sin(25.2^\circ) \approx 0.426 \]
Thus,
\[ \lambda \approx 2 \times 0.24 \times 0.426 \approx 0.20448 \text{ nm} \]
Now, for the second order (\( n = 2 \)):
\[ 2\lambda = 2d\sin\theta_2 \]
\[ \sin\theta_2 = \frac{2\lambda}{2d} \]
\[ \sin\theta_2 = \frac{\lambda}{d} \]
\[ \sin\theta_2 = \frac{0.20448}{0.24} \approx 0.852 \]
Thus,
\[ \theta_2 = \sin^{-1}(0.852) \approx 58.4^\circ \]
### Part (b): Wavelength of X-rays
From the first-order calculation:
\[ \lambda \approx 0.20448 \text{ nm} \]
Therefore:
- The second order will be observed at approximately \( 58.4^\circ \).
- The wavelength of the X-rays is approximately \( 0.20448 \) nm.
Yunus ghausi, P.E, T.E, PPM, MS,
Yunus.ghausi@outlook.com
Thank you sir for all ur efforts love ur videos and wish ur welll being and good health
Q-1) The answer can be easily found from the Bragg Diffraction Formula given by:
n*lambda = 2d*sin(theta)
In this case, because of the first order diffraction is happening at n=1, putting the number gives us:
1*lambda = 2*0,24 nm*sin(26,2°)
lambda=0,211 nm
Q-2) In this case, the second order diffraction is asked and it means that n=2
2*0,211 nm = 2* 0,24 nm *sin(theta)
theta = arcsin(0,211/0,24) = 61,54°
I hope I didn't do a mistake😅
Sir, there isn't anyone who can even be close to you in teaching and arouse curiosity abot physics and you are the best one in this field!!
When 4,5 years ago, I was in trouble because no one could teach us physics good and in an "intuitively pleasing" manner. And I couldn't find answers tı my questions. Then I found you and my life is entirely changed by your 8.02 lectures. I decided to study electrical engineering, which is a very nonintuitive area. Because you made me understand the electromagnetism even through it is a very non intuitive and a hard field.
You did a "magic touch" to me, and I believed you effected a lot of students like me in a positive way all around the world. I think that UN should give you a kind of prize!!
I apologize on my part to not watch all of your scientific problem solving videos, I will try to watch them more often. You should definetely continue to do these videos!!
WE ARE ALL YOUR STUDENTS SIR. WE ARE WALKING IN THE PATH THAT YOU OPENED AND TO THE GOAL THAT YOU SHOWED.
"Gratings" (😂) from Türkiye 🇹🇷
A)62 degrees
B)2.119 Angstroms
Bragg’s law: n* λ = 2d * sin θ. First order n= 1
λ = 2d * sin θ = 2 * 0,24nm * sin (26.2) = 0,21 nm (answer to b)
Second order n = 2
Sin θ = (2λ/2d) = 0,42/0,48 = 0,875
θ = arcsin(0,875) = 61 degrees (answer to a)
Using Bragg's Law nλ=2dsin(θ) The second-order diffraction will be observed at an angle of approximately 62.01 degrees, The wavelength of the X-rays is approximately 0.212 nm.
Second order angle is approximately 62°
And the wavelength of the x-rays is 0.105 nm approximately 1 angstrom
Bragg’s Law: 2d sin θ = nλ
First order angle θ₁ = 26.2°
n = 1
d = 0.24 nm
λ = (2d sin θ₁)/n
=> λ = 2×0.24×sin(26.2°)/1 ≈ 0.21 nm
Second order angle θ₂:
n = 2
d = 0.24 nm
λ = 2d·sin θ₁
2d·sin θ₂ = 2(2d·sin θ₁)
sin θ₂ = 2·sin θ₁
θ₂ = arcsin(2·sin θ₁)
θ₂ = arcsin[2×sin(26.2°)] ≈ 62°
Answer (a): Second order angle ≈ 62°
Answer (b): Wavelength ≈ 0.21 nm
λ = 1,06x10-11 m
θ = 62°
Sir l truly love physics but don’t forget the creator of all the omega,God
Quite unlike a 'Walter Lewin' problem. Just plugging numbers into an equation.😛
I agree - next problem will be more like a Walter Lewin problem
Greetings to you, Sir!
a) θ2 ≈ 62°
b) λ≈0,21nm
Meanwhile Indians already studied these all only for their college's entry exam called JEE ADVANCED 🗿👽
Oh boy, I'm making a mess of this compared to other's answers. Is theta here the complement of the angle in the lecture? Should the second order angle then be smaller than the first order as defined here? Is the spacing here perpendicular to the spacing in the optical grating in the lecture?
I like that you are trying to understand where Bragg's Law comes from.
Ask yourself how does a vertical row of atoms compare to a vertical row of slits. Think Huygens sources. Then think about the condition needed for constructive interference. WL covers this and also in his 8.03 Lect 21.
I looked up the diagram online and I see that my path diagram was wrong somehow. Now I get lambda = 2dsin(theta) = 0.2119... nm and theta2 = arcsin(lambda/d) = 62.0078... degrees
Still puzzling why my diagram was wrong.
Love you sir ❤❤❤
Waiting for problem 235❤❤❤
Hello sir
Hope you are doing well
How does image formation happen in water i mean i have seen the image of house which looks like its inverted in water and position of it seems just down the actual house
Is it same as concave mirrors
Does water also have focus and centre of curvature etc is the image forming on the centre of curvature
I am confused , is there any connection btw concave mirrors and this image formation in water
I'm sorry
I'm not good at explaining my questions
But i hope you got it
not the same at all - use google
@@lecturesbywalterlewin.they9259 i went through few websites but I am not able to imagine it
How reflection? Well , I haven't even properly understood reflection , I just know it's bouncing back of light...but what does it actually mean ,how is it forming images
I can't find the right source
But thank you
I'll Try to find out
Is it not forming real inverted image ?
There is no focus etc for water image ?
It's basically just a nature of geometry.If you cast two parallel rays,one ray from the top of a house and one ray from the bottom.Then when they get reflected,the bottom ray always get higher than the top ray,it's just geometry.Why parallel rays?All points in space emit so many arbitrary rays but only parallel rays got focus in at the focal plane equal a distance of focal length(infinity focus means all far objects have more absolute parallel rays than closer objects).And you can imagine like this: each point in infinity would have different poisitions in x and y on the focal plane but they share the same z(focal length).The reason you see the house image from the water reflection is your eyes are convex lenses,without the biological lens you can't see the image being formed.
Good evening sir from India 😊.
Sir,
I am Soumyadip Maity, an engineering student from India. In 8.02 spring 2002 Electricity and Magnetism, you told us(your TH-cam students) to study a book by
D. C Giancoli.
But I can't find the eBook of this book recommended by you.
Sir, I will be grateful to you if you give me the link to the book.
8.01
Physics
Hans C. Ohanian
Physics
Volume 1
2nd edition
W.W. Norton & Company
ISBN 0-393-95748-9
8.02
Physics for Scientists & Engineers by Douglas C. Giancoli.
Prentice Hall
Third Edition
ISBN 0-13-021517-18
8.03
Vibrations and Waves by
Anthony French
CRC Press
ISBN 9780748744473
8.03
Electromagnetic Vibrations, Waves and Radiation
by Bekefi and Barrett.
The MIT Press
ISBN 0-262-52047-8
---
Hello sir !!
Hru?
SIR WHY POWER SUPPLY IS A MULTIPLE OF 11 LIKE 110V THEN 220 V. IS THERE ANY REASON FOR THIS?
I HOPE YOU REPLYY
yes there are reasons for this - use google
Please Do not stop it, please
Heloo sir
where do you live?
What books and authors do you like and read?
Thank you for your answer😊😊😊❤❤❤❤
Sir my question is how to be consistent
Helooo sir how can i get your book for the love of physics :)
We love u
Vraag van mijn dochter in het kader van dierenartsopleiding mbt rontgenbuizen : " als je een elektronenversnelling onder een spanning van 100 volt zet dan hebben die elektronen toch ook 100 elektronenvolt??"
Weet U het ?
correct
@@lecturesbywalterlewin.they9259 ha... dank van mijn dochter. Heet trouwens ook Emma .... ze moet nog 1.5 jaar in utrecht.. 6 jaar opleiding en ze moest onderweg nog een jaar wachten vanwege plaatsgebrek ....
theta_2 = 62.0°
lambda = 0.21 nm
Seems like it is the last video of sir. Sir is surely saying "End of my Era" indirectly in the video 😢😭
Noooooooo sir please no!?
2dsintheta = nlambda
Substitute and solve
Sir ❤❤❤❤
Very good sir
Hii sir
halo
First
First answer is 0.211922809 nm
2nd anwer is 61.54
I got 99 problems but Bragg Diffraction ain't one