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University of Wisconsin - Milwaukee

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Problem 52 Hard Difficulty

Monochromatic light is beamed into a Michelson interferometer. The movable mirror is displaced 0.382 mm, causing the central spot in the interferometer pattern to change from bright to dark and back to bright N = 5 1 700 times. (a) Determine the wavelength of the light. What color is it? (b) If monochromatic red light is used instead and the mirror is moved the same distance, would N be larger or smaller? Explain.

Answer

a. \text { See explanation for result. }
b. \text { See explanation for result. }

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Video Transcript

So in this problem, actually, on the problems in the problem statement on the computer there's a type of here instead of end being 1700 on the computer, it is said that and equals 51 700. So I'm just going to follow the textbook where it is written and nickels and psychological 1700. All right, so let's begin the problem. So it is given that for Michael's an interferometer, the total distance moved by the mirror is 0.382 millimeter and this actually causes wth e total friends shift between bright to dark. Too bright. That one cycle equals total friend cycle of 1700 cycles. Okay. Ah, What that means is for bright to dark equals one French is going to be two times 1700 equals 3400 friendships in total. Right. So to solve the problem, which is to find the web link of the light, we should remember that one French shift is going to be caused by the Lambda before distance move of the mirror. Okay, so that means and friend shift is going to be caused by and times lambda before distance of the mirror, right so this distance here is also equivalent to the total distance moved by the mirror, which is l. So let's go to the next page. I'm going to rewrite this. L equals and times slammed up before. So from here we can see that Lambda is going to be four l over end, right? And that's gonna be four times 0.382 times 10 to the negative, three over. And he goes 3400. And this is going to give me 449 Madam eater. So this web link corresponds to blue light now for part B. Let's say instead of using blue light if we used red light, what happens to the total number of cycles, whether it gets larger or smaller. So to find that out, we just use this here. All right, so you can see that and is actually inversely proportional to were blinked, Right? So this also means and cycles is inversely put personal, too Web link. So that means if Lambda Red is greater than Lambda Blue, which is true, right? So I know that Lambda raid is greater than Lambda Blue. This means and cycles for raid should be smaller than and cycles for blue

University of Wisconsin - Milwaukee
Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Meghan M.

McMaster University