Find the angular width of the central maximum.

AI Thread Summary
The discussion revolves around calculating the angular width of the central maximum in a single-slit diffraction pattern. The initial calculation used the formula θ = λ / b, resulting in an angular position of 19.1°, but the correct angular width is 38.9°. Participants clarify that the total angular width should account for both minima on either side of the central maximum, leading to a calculation of 2θ. A suggestion is made to use the equation sin θ = λ/d for more accurate results, especially for small angles. A request for a valid resource link is also made to assist with further calculations.
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Homework Statement


A single slit of width 1.50 * 10-6m is illuminated with light of wavelength 500.0 nm. Find the angular width of the central maximum.

Homework Equations


θ = λ / b

The Attempt at a Solution


b = 1.50 * 10-6m
λ = 5.000 * 10-7
θ = λ / b = 0.333 = 19.1°

But the answer is 38.9°.

All my calculation of diffraction on single slit is off-target. It seems there is a fundamental point that I am missing. Please help. :frown:
 
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You have found the angular position,measured from the centre,of the pattern.There are two such minima,one on each side of the central maxima.
 
Last edited:
OK.. so what I need is 2Θ, right? Then I got 38.2, and this is a bit off from 38.9. Where did this difference come from?
 
I calculated it to be 38.9.The equation is:
sin theta=lambda/d.
Did you take theta to be in radians?If so that is a good approximation but only for very small angles.
 
I had a similar problem and was given this link.
http://www.calctool.org/CALC/phys/optics/fNA
It is a great link and solved my problem with units
 
Now I can solve the problems. Thanks everyone! :D

p.s. Emily, the link is not valid. Could you give me a right one? I can solve the problems, but still I want to check it out.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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