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

[somecelxis]

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?

 

[TSny]

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?

 

[desmond iking]

I guess the op means the distance between two first min is x ?

 

[somecelxis]

In the working above I assume the x is distance between two first minimum... Anything wrong with it?

 

[ehild]

x is the distance of any of the first minima from the central maximum.

ehild