Solved: Width of Slit with Monochromatic Light 550nm is 0.055mm

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Homework Help Overview

The problem involves the diffraction pattern produced by monochromatic light of wavelength 550nm passing through a narrow slit, with a converging lens used to focus the pattern onto a screen. The original poster states that the separation between the first minima is 10.0mm and seeks to determine the width of the slit, which they claim to be 0.055mm.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the formula x = λD/a, questioning whether it represents the distance between two first-order minima or the distance from the central maximum to one of the first-order minima. The original poster's interpretation of x is also examined.

Discussion Status

The discussion is ongoing, with participants clarifying the meaning of the variable x in the context of the problem. There is no explicit consensus on the interpretation of the formula or the original poster's calculations, but guidance is being offered regarding the definitions involved.

Contextual Notes

There is uncertainty regarding the definition of the distance x in the formula and whether it aligns with the problem's description of the minima. The original poster's calculation of the slit width is also under scrutiny.

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Homework Statement


Monochromatic light of wavelength 550nm is used to illuminate normally a narrow slit. A converging lens of focal length 50cm is used to focus the diffraction pattern onto a screen. If the separation between the first minima is 10.0mm What is the width of the slit. The ans is 0.055mm.


Homework Equations





The Attempt at a Solution


by using formula x= λD/ a ,
i have 10x10^-3 = (550x10^-9) x ( 50x10^-2) / (a) ,
i get my a = 0.0275mm ... What's wrong with my working?
 
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somecelxis said:
by using formula x= λD/ a ...

Is this formula meant to give the distance between the two first-order minima or is it meant to give the distance between the central maximum and one of the first-order minima?
 
I guess the op means the distance between two first min is x ?
 
In the working above I assume the x is distance between two first minimum... Anything wrong with it?
 
x is the distance of any of the first minima from the central maximum.

ehild
 

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