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

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The discussion revolves around calculating the highest observable order number for a grating illuminated with 585 nm light and having 1483 lines/cm. The formula involves determining the grating spacing (d) and ensuring that the sine of the angle (theta) does not exceed 1. The calculation leads to an order number (m) of 11.5, prompting a clarification that only integer values are valid for observable orders. The conversation emphasizes the importance of constructive interference at specific points on the viewing screen. Understanding the relationship between the grating lines and light interference is crucial for solving the problem correctly.
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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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