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A pair of red lights mounted 1 meter apart are far enough away that they are bar

ID: 2113506 • Letter: A

Question

A pair of red lights mounted 1 meter apart are far enough away that they are barely resolvable as two sources. A similar pair of blue lights (also 1 meter apart) is also mounted far enough away as to be barely resolvable. Which pair of sources is farthest from the observer? Justify your answer

theta = D/L            

red light is 650 nm

blue light is 475 nm

I'm not setting this up right, or I'm using the wrong formula (or I need a second formula). Please show how you would solve it and explain. (the last person explained it great-I was missing a point, but I couldn't solve this on a test is presented with something similar). Thanks!

Explanation / Answer

The blue lights. Blue light has a shorter wavelength than red. Since the size of the Airy disk is more or less proportional to the wavelength, and the size determines resolution, the blue lights must be resolved with a smaller angle than the red. Since both lights are 1m apart, the blue lights must be further away, to create a smaller angle.

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