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

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In summary, the highest order number that can be observed is 11 when a grating with 1483 lines/cm is illuminated with light of wavelength 585 nm, since the sine of theta can never be greater than 1 and the maximum value of m is 11. The additional step is to multiply m by the wavelength and divide by the distance between lines to find the highest order number. However, in this case, the answer was wrong because 11.5 is not an integer and therefore, not a possible value for m.
  • #1
mustang
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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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  • #2
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.
 
  • #3
Regrads on the problem

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?
 
  • #4
Is 11.5 an integer?
 
  • #5
What are you trying to say in "Is 11.5 an integer?"
 
  • #6
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?
 

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

1. What is the significance of "585 nm" in "Problem23: Highest Order for 585 nm Grating w/1483 Lines/cm"?

The "585 nm" refers to the wavelength of light that the grating is designed to diffract, which is in the visible spectrum. This specific wavelength may be important for certain experiments or applications.

2. What does "1483 Lines/cm" mean in the context of this problem?

The "1483 Lines/cm" refers to the number of lines per centimeter on the grating. This is a measure of the spacing between the lines on the grating and can affect the diffraction pattern produced.

3. How is the highest order determined for this grating?

The highest order is determined by the formula "highest order = (number of lines per cm) x (wavelength of light in nm) / 10". In this case, the highest order is 88.

4. What is the significance of the highest order for a grating?

The highest order is the maximum diffraction order that the grating can produce. This means that after the light is diffracted through the grating, it will have 88 distinct diffraction angles based on the spacing of the lines on the grating.

5. Can the highest order be increased by changing the grating's specifications?

Yes, the highest order can be increased by either increasing the number of lines per centimeter on the grating or decreasing the wavelength of light. However, this may also affect the diffraction efficiency and overall quality of the diffraction pattern produced.

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