In order to check the spacing between two gears in a miniature motor, you shine

Question

In order to check the spacing between two gears in a miniature motor, you shine a laser light with wavelength 530nm through the gap between them.
A)measuring the diffraction pattern, you determine that the central maximum is 0.12, radians wide. What is the width of the gap between gears?
B)It's generally easier to measure larger distances. Will you get more accurate results for gap spacing if this experiment is done under water? Why/why not?

Please explain clearly and show each step/equations that you use to help me understand. Full karma points awarded.

Explanation / Answer

A) let the central max is ?(rad) the gap distance be d. d*?/2=lambda so d=8833(nm) B) underwater, the wavelength of light is shorter = lambda/n so that mean ? will be smaller which will be harder to measure.

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