How do I find the spacing(d) of a grating in a diffraction grating experiment.

In summary, the conversation discusses question 7b from a physics homework assignment, which involves using the equation dsin∅=nλ to solve for the value of ∅. The student subtracted two angles and plugged the values into the equation, but their answer was half of the expected answer. The conversation also mentions a figure and the importance of understanding the angle ∅ in this context. The question ultimately asks why the answer sheet uses an angle of 13 degrees instead of the 26 degrees calculated by the student.
  • #1
mutineer123
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0

Homework Statement



http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9702%20-%20Physics/9702_s02_qp_2.pdf

question no. 7b





Homework Equations



dsin∅=nλ





The Attempt at a Solution



I subtracted the two angles and got 26 degrees. So then I plugged it all into the equation:
dsin26=2 X 630x10^-9.
My answer is half the actual answer because the angle the answer sheet has is 13 degree. Why do they take it as 13 degree??
 
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  • #2
Look at the figure. The two angles correspond to the second-order maxima at both sides of the central maximum.
You need to know what angle is called ∅. ehild
 

1. How does the number of lines in a grating affect the spacing?

The number of lines in a grating, also known as the grating density, directly affects the spacing (d) of the grating. The higher the grating density, the smaller the spacing will be between each line. This is because a higher density means more lines are packed into the same area, resulting in a smaller distance between each line.

2. How is the spacing (d) of a grating calculated?

The spacing (d) of a grating can be calculated using the equation d = sinθ / mλ, where θ is the angle of diffraction, m is the order of diffraction, and λ is the wavelength of the incident light. This equation is known as the grating equation and is derived from the relationship between the angle of diffraction and the spacing of the grating.

3. Can the spacing (d) of a grating be changed?

Yes, the spacing (d) of a grating can be changed. It can be altered by either changing the grating density or by changing the wavelength of the incident light. As mentioned before, a higher grating density results in a smaller spacing, while a longer wavelength of light will also result in a smaller spacing.

4. Why is the spacing (d) of a grating important in a diffraction grating experiment?

The spacing (d) of a grating is important in a diffraction grating experiment because it determines the angles and intensities of the diffracted orders. The spacing affects the diffraction pattern produced by the grating, which is used to analyze the properties of the incident light, such as wavelength and polarization.

5. How does the spacing (d) of a grating affect the resolution of a diffraction grating experiment?

The spacing (d) of a grating is directly proportional to the resolution of a diffraction grating experiment. This means that a smaller spacing will result in a higher resolution, allowing for more precise measurements to be made. This is because a smaller spacing produces a larger angle of diffraction, resulting in a more spread-out and clear diffraction pattern.

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