Finding Central Maximum Width for Laser

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Homework Help Overview

The problem involves a laser with a wavelength of 632.8 nm passing through a single slit of width 0.30 mm, and the goal is to determine the width of the central maximum on a screen located 1.0 m behind the slit.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the equation asin(theta) = m lambda and explore the calculation of sin(theta) for the first minimum. There is an attempt to find the angle theta using the inverse sine function, and questions arise regarding the interpretation of the sine function in relation to angles.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to proceed after calculating sin(theta). There is an exploration of trigonometric relationships to find the height corresponding to the central maximum, but no consensus has been reached on the next steps.

Contextual Notes

Participants express uncertainty about the process of converting sin(theta) values into angles and how to apply trigonometric properties to find the desired dimensions on the screen.

xswtxoj
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Homework Statement



A laser 632.8nm is sent through a single slit of widith 0.30 mm. Wats the width of the central maximum on a screen 1.0m in the back of the slit?

Homework Equations



asin(theta) = m lamda

The Attempt at a Solution


lamda: 632.8nm

0.30 mm= 3.0 x 10^-4 m

sin(theta)= m lamda/ a
sin(theta)= 1 (632.8x10^-9)/3.0 x 10^-4 m

= 2.10x10^-3 m
 
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xswtxoj said:

Homework Statement



A laser 632.8nm is sent through a single slit of widith 0.30 mm. Wats the width of the central maximum on a screen 1.0m in the back of the slit?

Homework Equations



asin(theta) = m lamda

The Attempt at a Solution


lamda: 632.8nm

0.30 mm= 3.0 x 10^-4 m

sin(theta)= m lamda/ a
sin(theta)= 1 (632.8x10^-9)/3.0 x 10^-4 m

= 2.10x10^-3 m


Ok you're on the right track, you found sintheta. Now use your inverse sin function and find the angle theta. Once you have that, you know the distance to the screen. Can you find a basic trig property to help you find the unknown "height" if you will of the screen? (remember, this height you find will only be half the width of the central maximum)
 
do i inverse sin 2.10 E -3? I'm nto quick sure what to do?
 
xswtxoj said:
do i inverse sin 2.10 E -3? I'm nto quick sure what to do?

You don't know how to turn SinTheta = x into an angle?

What Theta corresponds to SinTheta = 1/sqrt2 for example?
 

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