Help explain the following formula? (Young's doubles slit)

[KneelsBoar]

Hello, I'm currently writing a report on young's double slit experiment, and I've used the equation nλ/d = x/L and I was wondering if someone could explain the question? I know how it works, and how to solve for lambda, but could I have some more detail into why it works?

For example, why can Sin θ be substituted by x/L in this case? Would they not give different values?

I appreciate the help.

 

[SammyS]

Hello, I'm currently writing a report on young's double slit experiment, and I've used the equation nλ/d = x/L and I was wondering if someone could explain the question? I know how it works, and how to solve for lambda, but could I have some more detail into why it works?

For example, why can Sin θ be substituted by x/L in this case? Would they not give different values?

I appreciate the help.

Hello KneelsBoar. Welcome to PF !

Can you supply a sketch with those quantities included?

 

[physics user1]

So, in the limit L>>d you have this equation for young double slit constructive interference:

dsin θ = nλ

Sin θ = nλ/d

Now, if λ/d is small or in other words d is much larger than lambda also sin θ is small

If the sine is small it can be approximate by the tangent that is x/L if by x you mean the vertical distance between the center and the fringe

So yes... x/L is different by the sine, but if you consider small angles the sine can be approximate by the tangent and then by x/L

Example: use the calculator to find sin (2) and tan (2) ( i mean 2 degrees not 2 radians)

 

[mukundpa]

As the value of x (in mm) is very small as compared to the screen distance L (in m) the angle theta is very small and for small angles sine of that angle is approximately equal to the angle measured in radius.
Alternately for very small angle the arc length and the perpendicular is nearly same and thus theta = arc length/ radius = perpendicular/ hypotenuse