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

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The discussion revolves around calculating the width of a slit using monochromatic light of wavelength 550nm and a converging lens with a focal length of 50cm. The user initially applied the formula x = λD/a but misinterpreted the variable x, assuming it represented the distance between the first minima rather than the distance from the central maximum to the first minima. Clarification is sought on whether the formula is intended for the distance between two first-order minima or from the central maximum to one of the minima. The correct interpretation leads to the conclusion that the width of the slit is 0.055mm. This highlights the importance of accurately defining variables in diffraction problems.
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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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