Problem23: Highest Order for 585 nm Grating w/1483 Lines/cm

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Homework Help Overview

The problem involves a diffraction grating illuminated by light of wavelength 585 nm, with a specified number of lines per centimeter (1483 lines/cm). The goal is to determine the highest observable order number for the diffraction pattern, considering the physical constraint that the sine of the angle cannot exceed 1.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between the wavelength, the number of lines, and the maximum order of diffraction. Some suggest using a formula to find the maximum integer order, while others question the interpretation of results, particularly regarding the integer nature of the order number.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions made about the integer nature of the order number. Some guidance has been offered regarding the relationship between the grating lines and the diffraction pattern.

Contextual Notes

There is a focus on the physical limitations of the sine function in relation to the diffraction orders, and participants are considering the implications of the calculated order being a non-integer value.

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Problem23. A grating with is illuminated with light of wavelength 585 nm. What is the highest order number that can be observed if the grating has 1483 lines/cm? remember sin(theta) can never be greater than 1.
 
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C'mon. Just plug into the formula.

He gave you λ and it takes just one division to find d. You know that sin(ANYTHING) can't be greater than 1. So what is the biggest integer m that gives you a sin less than 1? Then there's just 1 more step. I'm sure you can figure that out.
 
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So the answer would be:
m*(585 nm)
sin(theta) = 1 = ------------
6743 nm/line

Multiply both sides by 6743 to get:

6743 = m * 585

Then divide both sides by 585 to get:

m = 6743/585 = 11.5
But when i checked the asnwer was wrong?
 
Is 11.5 an integer?
 
What are you trying to say in "Is 11.5 an integer?"
 
Let's take it one step at a time.

Do you understand what the lines represent?

In other words, do you realize that the lines appear on the viewing screen only at points where light rays coming through different slits interfere constructively with each other?
 

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