Solving Diffraction Problem: Calculating Slit Width with He-Ne Laser

[Naeem]

Q. A He-Ne laser of wavelength (633nm) shines thru a single slit of unknown width D on to screen 2.0m away from the slit. The distance on the screen between the m = 1 minima on either side of the central maximum of the diffraction pattern is measured and is found to be 2.3 cm. What is the width of the slit?

Ans. I did,
ym = wavelength * D/d

Is this right.

Please help, me folks...

 

[xanthym]

Q. A He-Ne laser of wavelength (633nm) shines thru a single slit of unknown width D on to screen 2.0m away from the slit. The distance on the screen between the m = 1 minima on either side of the central maximum of the diffraction pattern is measured and is found to be 2.3 cm. What is the width of the slit?

{Distance From Central Maximum To First Minimum On Screen} = M =approx= λY/D
where "λ" is the wavelength, "Y" the distance to screen, and "D" the single slit width. For this problem, we are given {λ = 633e(-9) m}, {Y = 2 m}, {M = (2.3 cm)/2 = 0.0115 m}, so that:
D = λY/M = {633e(-9)}*(2)/(0.0115) = {1.1e(-4) m} = (110 μm)


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[davidY]

if you are confused about that i think that he used:

dsin(theta)=m*lambda
and for small theta
sin(theta)=tan(theta)
and in this case, tan(theta)=Size projected on screen/distance to screen