q_a_assignment17

course Phys 202

How do you work number 4 in chapter 24. I have:

lambda=6.56*10^-7m

d=6.0*10^-5m

i used the first order to determine a angle.

dsin(theta)=m*lambda

6.0*10^-5msin(theta)=1*6.56*10^-7m

theta=.626

Where do I go from here?

Remember that I don't always have the text handy when I respond to your work. I generally need at least an outline the statement of the problem.

Fortunately I do have the book handy this time.

You give the angle as .626. This isn't correct. The angle is about .011. Any angle given without units is in the default unit, which is radians. If you use any other unit (and in this case the radian is the easiest unit to use), you have to include the unit.

.011 radians = .63 degrees, approximately, so you appear to have given the angle in degrees.

At a distance of 3.6 meters from the slits, the unknown distance (let's call it x) is related to theta by

x / 3.6 meters = tan(theta).

A picture of the situation should make this clear; let me know if it doesn't, but the 3.6 meters is perpendicular to the distance x between lines, so x and 3.6 meters form the opposite and adjacent sides of a right triangle with base angle theta.

So x = 3.6 meters * tan(theta).

For small angles, tan(theta) = theta is a very good approximation, so we have

x = 3.6 meters * tan(.011) = 3.6 metes * .011 = .0396 meters, approximately. A closer approximation of .011 would give you a more precise result.

This would also work if you used theta = .626 degrees.

assignment #017

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Physics II

07-20-2006

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19:50:49

General College Physics and Principles of Physics Problem 24.2: The third-order fringe of 610 nm light created by two narrow slits is observed at 18 deg. How far apart are the slits?

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RESPONSE -->

m=3

lambda=6.10*10^-9m

theta=18

dsin(theta)=m*lambda

d=(m*lambda)/sin(18)=5.92*10^-6

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19:51:15

The path difference for a 3d-order fringe is 3 wavelengths, so light from one slit travels 3 * 610 nm = 1830 nm further.

The additional distance is equal to slit spacing * sin(18 deg), so using a for slit spacing we have

a sin(18 deg) = 1830 nm.

The slit spacing is therefore

a = 1830 nm / sin(18 deg) = 5920 nm, or 5.92 * 10^-6 meters.

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RESPONSE -->

I got the same answer and I know how to do that problem.

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19:55:58

**** query gen phy problem 24.7 460 nm light gives 2d-order max on screen; what wavelength would give a minimum?

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RESPONSE -->

4.6*10^-9=lambda

m=2

I don't know what it means exactly by max and min and how that fits into the problem

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20:00:17

STUDENT SOLUTION FOLLOWED BY INSTRUCTOR COMMENT AND SOLUTION:

The problem states that in a double-slit experiment, it is found that bule light of wavelength 460 nm gives a second-order maximun at a certain location on the screen. I have to determine what wavelength of visible light would have a minimum at the same location. To solve this problem I fist have to calculate the constructive interference of the second order for the blue light. I use the equation dsin'thea=m'lambda. m=2

(second order)

dsin'thea=(2)(460nm)

=920nm

Now, I can determine the destructive interference of the other light, using the equation

dsin'thea=(m+1/2)'lambda=(m+1/2)'lambda m+(0,1,2...)

Now that I have calculated dsin'thea=920nm, I used this value and plugged it in for dsin'thea in the destructive interference equation.(I assumed that the two angles are equal) because the problem asks for the wavelength at the same location.

Thus,

920nm=(m+1/2)'lambda. m=(0,1,2,...)

I calculated the first few values for 'lambda.

For m=0 920nm=(0+1/2)'lambda

=1.84*10^nm

For m=1 920nm=(1+1/2)'lambda =613nm

For m=2 920nm=(2+1/2)'lambda=368 nm

From these first few values, the only one of thes wavelengths that falls in the visible light range is 613nm. Therefore, this would be the wavelength of visible light that would give a minimum.

INSTRUCTOR COMMENT AND SOLUTION: good. More direct reasoning, and the fact that things like sines are never needed:

** The key ideas are that the second-order max occurs when the path difference is 2 wavelengths, and a minimum occurs when path difference is a whole number of wavelengths plus a half-wavelength (i.e., for path difference equal to 1/2, 3/2, 5/2, 7/2, ... of a wavelength).

We first conclude that the path difference here is 2 * 460 nm = 920 nm.

A first-order minimum (m=0) would occur for a path difference of 1/2 wavelength. If we had a first-order minimum then 1/2 of the wavelength would be 920 nm and the wavelength would be 1860 nm. This isn't in the visible range.

A minimum would also occur If 3/2 of the wavelength is 920 nm, in which case the wavelength would be 2/3 * 920 nm = 613 nm, approx.. This is in the visible range.

A niminum could also occur if 5/2 of the wavelength is 920 nm, but this would give us a wavelength of about 370 nm, which is outside the visible range. The same would be the case for any other possible wavelength. **

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RESPONSE -->

It now makes sense. A max is constructive while a min is deconstructive and is a half a wavelength more. I have reworked the problem again with the solution as I guide and I am fairly sure that I understand the problem now.

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20:00:21

**** query univ phy problem 35.52 (37.46 10th edition) normal 477.0 nm light reflects from glass plate (n=1.52) and interferes constructively; next such wavelength is 540.6 nm.

How thick is the plate?

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20:00:24

** The path difference for constructive interference is an integer multiple of the wavelength. The path difference here is twice the thickness.

Wavelengths in glass are 477 nm / 1.52 and 540.6 nm / 1.52.

So we know that double the thickness is an integer multiple of 477 nm / 1.52, and also an integer multiple of 540.6 nm / 1.52.

We need to find the first integer multiple of 477 nm / 1.52 that is also an integer multiple of 540.6 nm / 1.52.

We first find an integer multiply of 477 that is also an integer multiply of 540.6.

Integer multiples of 540.6 are 540.6, 1081.2, 1621.8, etc. Dividing these numbers by 477 we obtain remainders 63.6, 127.2, etc. When the remainder is a multiple of 477 then we have an integer multiple of 477 which is also an integer multiple of 540.6.

SInce 477 / 63.6 = 8.5, we see that 2 * 477 / 63.6 = 17. So 17 wavelengths of 477 cm light is the first multiple that is equivalent to an integer number of wavelengths of 540.6 cm light.

17 * 477 = 8109.

Since 8109 / 540.6 = 15, we see that 17 wavelengths of 477 nm light span the same distance as 15 wavelengths of 540.6 nm light.

It easily follows that that 17 wavelengths of (477 nm / 1.52) light span the same distance as 15 wavelengths of (540.6 nm / 1.52) light.

This distance is 17 * 477 nm / 1.52 = 5335 nm.

This is double the thickness of the pane. The thickness is therefore

pane thickness = 5335 nm / 2 = 2667 nm.

IF INTERFERENCE WAS DESTRUCTIVE: n * 477 nm / 1.52 = (n-1) * 540.6 nm / 1.52, which we solve:

Multiplying by 1.52 / nm we get

477 n = 540.6 n - 540.6

n * (540.6 - 477 ) = 540.6

n * 63.6 = 540.6

n = 540.6 / 63.6 = 8.5.

This is a integer plus a half integer of wavelengths, which would result in destructive interference for both waves.

Multiplying 8.5 wavelengths by 477 nm / 1.52 we get round-trip distance 2667 nm, or thickness 1334 nm. **

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20:00:26

**** query univ phy prob 35.50 (10th edition 37.44): 700 nm red light thru 2 slits; monochromatic visible ligth unknown wavelength. Center of m = 3 fringe pure red. Possible wavelengths? Need to know slit spacing to answer?

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RESPONSE -->

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20:00:28

STUDENT SOLUTION: The pure red band at m = 3 suggests that there exists interference between the wavelength of the red light and that of the other light. Since only the red light is present at m = 3 it stands to reason that the wavelength of the other light is a half of a wavelength behind the red wavelength so that when the wavelength of the red light is at its peak, the wavelength of the other light is at its valley. In this way the amplitude of the red light is at its maximum and the amplitude of the other light is at it minimum – this explains why only the red light is exhibited in m = 3.

INSTRUCTOR COMMENT

At this point you've got it.

At the position of the m=3 maximum for the red light the red light from the further slit travels 3 wavelengths further than the light from the closer. The light of the unknown color travels 3.5 wavelengths further. So the unknown wavelength is 3/3.5 times that of the red, or 600 nm.

You don't need to know slit separation or distance (we're assuming that the distance is very large compared with the wavelength, a reasonable assumption for any distance we can actually see. **

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This looks good. See my answer to your question and let me know if you need more clarification.