- #1

lulzury

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## Homework Statement

A monochromatic light source is used with a double slit to create an interference pattern on a screen that is 2.00 meters away. If the 2nd bright spot is observed 8.73 mm above the central maximum, can the small angle approximation be used? Show and/or explain your reasoning

## Homework Equations

## d\sinθ=mλ ##

## The Attempt at a Solution

I might be over-thinking this. I know you can have a small angle approximation if D >> d, but in this case I don't know d yet, so I first wanted to relate d to y without first assuming a small angle approximation (sinθ ≈ tanθ ≈ θ), but I get stuck:

I get the following relation:

## D=\frac{d}{2\tan(γ)} ##

## D= (y+\frac{d}{2}) * \frac{1}{ \tan(θ)} ##

## \frac{d}{2}\cot(γ) = y\cot(θ) + \frac{d}{2}\cot(θ) ##

I'm not sure how to solve for d here so that I can show that D >> d.

Thanks in advance!