### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Physics III PH 113

RHIT

GPA 3.69

### View Full Document

## 9

## 0

## Popular in Course

## Popular in Physics 2

This 9 page Class Notes was uploaded by Jalon Willms on Monday October 19, 2015. The Class Notes belongs to PH 113 at Rose-Hulman Institute of Technology taught by Michael Moloney in Fall. Since its upload, it has received 9 views. For similar materials see /class/225109/ph-113-rose-hulman-institute-of-technology in Physics 2 at Rose-Hulman Institute of Technology.

## Reviews for Physics III

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/19/15

Interference of two sources April 28 2008 MJM Suppose we have two sources of ultrasonic waves The wavelength of these source is 800 mm and the sources are in phase at s1 and sz Si p1 s2 r2 p2 If we are at point p1 equidistant from the sources there is constructive interference and a large signal in the detector we have there The waves have the same frequency f and angular frequency 03 21Tf They travel at the same speed and have the same wavelength 7 and propagation constant k 2110 The disturbances at p1 are y1Acosntkr1 and yzAcos oater The phase 4 of each wave is the argument of the cosine 1 mt km and 412 mt kr2 The phase difference is called I in the text phase difference I I 11 phase difference oat krz oat krl k r1 r2 phase difference k path difference 2110 path diference on p 1216 1 This is very important Waves of the same frequency and wavelength which start out in phase can get out of phase because they travel different distances to reach the point where they meet Question if the path difference between ultrasonic rays at point p2 was 400 mm would the detector there have a large signal or a small signal Will the rays be constructively interfering or destructively interfering The book on p 1209 discusses constructive and destructive interference between rays from s1 and sz When light rays interfere they often travel many many wavelengths to get where they are going and the angles involved are often very small like 120 of a degree For these cases we have an extremely useful formula for path difference which the text illustrates nicely on the bottom of p 1211 path difference d sin 0 2 where d is the separation of the sources and 0 is the angle that rays make to the perpendicular bisector of the line joining the sources Now suppose we put two slits separated by a distance d in a beam of coherent light discussed on p 1208 and the light from the slits falls on a screen 300 cm away from the slits The wavelength of the light is 650 nm or A 65x 10 7 m We will see a pattern of bright and dark on the screen like in the text on p 1213 Fig 357 At point some A where 0 0 there is a bright spot because the path difference is zero and the two arriving beams oflight are in phase At point B 050 cm from point A it is dark because the path difference causes the beams to be out of phase and at point C which is 100 cm from point A it is bright again since the beams are back in phase a What is the path difference of the arriving beams at point A the center where it s bright b What is the path difference of the arriving beams at point B next to A where it s dark c What is the path difference of the arriving beams arriving at point C next to B it s again bright d Calculate the angle 0 in a radians at point C remember that 0 0 at point A This is just trig knowing A and C are 100 cm apart and 300 cm from the slits e Knowing the path difference from c and the angle from d calculate the distance d between the two slits Using Eq 2 f What is the path difference halfway between A and B Interference of two sources April 28 2008 MJM Suppose we have two sources of ultrasonic waves The wavelength of these source is 800 mm and the sources are in phase at s1 and sz Si p1 s2 r2 p2 If we are at point p1 equidistant from the sources there is constructive interference and a large signal in the detector we have there The waves have the same frequency f and angular frequency 03 21Tf They travel at the same speed and have the same wavelength 7 and propagation constant k 2110 The disturbances at p1 are y1Acosntkr1 and yzAcos oater The phase 4 of each wave is the argument of the cosine 1 mt km and 412 mt kr2 The phase difference is called I in the text phase difference I I 11 phase difference oat krz oat krl k r1 r2 phase difference k path difference 2110 path diference on p 1216 1 This is very important Waves of the same frequency and wavelength which start out in phase can get out of phase because they travel different distances to reach the point where they meet Question if the path difference between ultrasonic rays at point p2 was 400 mm would the detector there have a large signal or a small signal Will the rays be constructively interfering or destructively interfering 7 800 mm and Ar 400 mm s0 Ar N2 The signal would be zero due to destructive interference The book on p 1209 discusses constructive and destructive interference between rays from s1 and sz When light rays interfere they often travel many many wavelengths to get where they are going and the angles involved are often very small like 120 of a degree For these cases we have an extremely useful formula for path difference which the text illustrates nicely on the bottom of p 1211 path difference d sin 0 2 where d is the separation of the sources and 0 is the angle that rays make to the perpendicular bisector of the line joining the sources Now suppose we put two slits separated by a distance d in a beam of coherent light discussed on p 1208 and the light from the slits falls on a screen 300 cm away from the slits The wavelength of the light is 650 nm or A 65x 10 7 m We will see a pattern of bright and dark on the screen like in the text on p 1213 Fig 357 At point some A where 0 0 there is a bright spot because the path difference is zero and the two arriving beams oflight are in phase At point B 050 cm from point A it is dark because the path difference causes the beams to be out of phase and at point C which is 100 cm from point A it is bright again since the beams are back in phase a What is the path difference of the arriving beams at point A the center where it s bright zero b What is the path difference of the arriving beams at point B next to A where it s dark N2 c What is the path difference of the arriving beams arriving at point C next to B it s again bright d Calculate the angle 0 in a radians at point C remember that 0 0 at point A This is just trig knowing A and C are 100 cm apart and 300 cm from the slits tan 6 0010 m 300 m 1300 5 0 e Knowing the path difference from c and the angle from d calculate the distance d between the two slits Using Eq 2 dsine7t65x10397m andsine 591300 d 300 x 65 x 10 7 m 195 x 10 4 m f What is the path difference halfway between A and B Ar N4 since for small angles when you cut the distance in half the angle cuts in half and the path difference cuts in half At C it was 7 and at A it was zero PH 113 Adding N disturbances reV April 29 2008 Suppose we have N disturbances like y1 E sin oat yz E sin oat p y3 E sin oat 21 Etc Each can be represented by a phasor E We39ll get the resultant Ep at some point p for N ofthese using N 3 as an example First we inscribe them in a circle of radius R The radius R will drop out at the end From the triangle including the light dotted lines we have EpZ R sin thZ N 3 for us From the triangle with the heavy dashed line we have E2 R sin p 2 When we diVide these two equations we get EpE sinNp2 sinp2 so nally Ep E sinNp2 sinp2 I is the phase difference between adjacent phasors over Remember Ep 2E cos cpZ That works for two phasors so we ll try N 2 N 2 Ep E sin 2 p2 sinp2 You remember that sin 6 2 sin 62 cos 92 so we ll put that in and get Ep E 2 sin p2 cos p2sinp2 2E cos ltp2 Now lets try N 3 and p 1t2 You did this in class for me The phasor diagram was E Ep E When we go into Ep E sinNq2 sinq2 with N 3 and q n2 we get Ep E sin 31t4 sin114 E If we try N 4 and q n4 what do we get Right They bite their own tail So now we have a recipe for adding N disturbances which have the same frequency and where there is a phase difference q between each one and the next A train39 of N of these disturbances will bite its own tail39 when the phase difference is 211N We tried this for N 3 in class and q 21t3 The phasor diagram was E E For 6 phasors we would form a hexagon when q 2116 and would get Ep 0 13 E sinNp2 sinp2 Ep E sin 6 21tl2 sin211l2 E sin11 sin211l2 0 Next page for a grating ofN slits N slit grating Using phase difference rstorder maximum N slit grating Using path dl erence Ar rstorder maximum Second order maximum NEXT PAGE FOR ANGLES 9 90 130 EpE0NE alla1rowslineupBIGMAX q 21tN Ep 0 N arrows bite own tail DARK SMALL STUFF Intensity not very great q 211 21tN bite own tail DARK q 211 Ep Na all arrows line up BIG MAX q 211 21tN bite own tail DARK MORE SMALL STUFF 90Ar0 EpNEE0 arrowslineupBIGMAX Ar MN Ep 0 N arrows bite own tail DARK SMALL STUFF Ar u MN bite own tail DARK Ar 2 Ep NE all arrows line up BIG MAX Ar 1 MN bite own tail DARK MORE SMALL STUFF Ar 27 BIG MAX Ar 2 MN bite own tail DARK N slit grating 9 0 q 0 9 0 all arrows line up BIG MAX Distance d between each slit d sin 9 MN Ep 0 N arrows bite own tail DARK Using angle 9 SMALL STUFF d sin 9 7w XN bite own tail DARK firstorder maximum 1 sin 9 2h Ep NE all arrows line up BIG MAX d sin 9 7t MN bite own tail DARK MORE SMALL STUFF secondorder maximum 1 sin 9 2 Ep NE all arrows line up BIG MAX thirdorder maximum 1 sin 6 3 Ep NE all arrows line up BIG MAX Grating max39s occur at 1 sin 6 m A Min39s next to max39s occur at 1 sin 0 m i MN the bigger N is the 39sharper39 the max39s are For a SINGLE SLIT slit width a N one bazillion The intensity will be zero when the train of N arrows bites its own tail This means a phase difference of 21Ip where p is an integer between the first and the last one the first is from the top of the slit and the 2quotd is from the bottom of the slit In our formula Ep E sinNq2sinp2 Nq 2 up The book uses N for the hase difference between the first and the last phasor q is very small so sinp2 E p2 2N Then Ep E sinNp2sinp2 E NE sini2 i2 E0 sini2 2 When i 211 the train of arrows bites its own tail and also for 411 611 etc For intensity I I0 sin 2 2 2 I 0 when i 211 411 611 etc The path difference from the top of a slit of width a and the bottom is Ar a sin 9 remember a is the width of the entire slit 5 21t7t path difrerence 21t7t Ar 21t7t a sin 9 middle p 1244 Sooo 15m 0 when a sin 9 p 2 p 0 l 2 etc 39fat slit ofwidth a object 40 mm fm vertex Find image from algebra And ray diagrams 9 mm for object cc30mm l l 1A 3 gt WSk m S O a center ofcurvature CC 41 mm object 51 mm to cc 3 28Ta quotb lgCka x l r i 4i k E 4 9 gt0 wlicn uhjcct ml same side as light cmcring s quot wlicn imqu on sumc side as light caving R 390 lllt39ll cc on same sidc as light leaving 39 of UM uturc 3 mm im cncx vcncx I T I v32 ii m 4 ELECT I EERL q MEIED

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.