A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10 -5 m

Question

A beam of light of wavelength 600 nm passes through a slit that is 3.1 × 10-5 m wide, and then goes on to a screen that is 2.2 m from the slit. On the screen, how far is the second dark fringe from the center of the diffraction pattern?

The correct answer is 8.5cm which I was able to deduce out of my options given because it was the only answer that had a .5 and I know that if its a dark fringe I'm looking at destructive interference and therefore a .5 will be in my answer.

however, I do not know how to figure this out with the question involving a single slit if you could please explain.

thank you for your time.

Explanation / Answer

Slit Width a = 3.1 * 10^-5 m
Distance between Screen and Slit L = 2.2 m
Wvelength = 600 nm

Second Diffraction Pattern Occurs at sinT = 2/a

Distance of Second Dark Fringe from Central Maximum is given by -
Y = L * 2* / a  
Y = 2.2 * 2*600 * 10^-9 / 3.1 * 10^-5
Y = 0.085 m
Y = 8.5 cm

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