Double-slit experiment question

[jairusgarcia]

The question goes like this,
From the 2-slit interference experiment, determine the position of the 1st maximum if lambda=400nm, d=1mm and D=10cm.

I've been reading through the experiment through external sites and none had given an example near the question. The question is, should i use Young's formula? What should i do first?

Thanks! ^_^

 

[mgb_phys]

Draw a diagram - it's just trig.
Put all the dimensions in the same units.

 

[jairusgarcia]

it's just trig.
Put all the dimensions in the same units.

how? i mean, draw a triangle and input the measurements? when the problem says find the maximum, is that the central maximum where n=0?

 

[Doc Al]

when the problem says find the maximum, is that the central maximum where n=0?

Since the central maximum is always in the center, that wouldn't be much of a challenge, would it? The first maximum means the first non-central maximum: where m = 1 (or n = 1, depending on your notation) in the Young's double slit formula. (Read this: Double Slit Interference)

 

[jairusgarcia]

ok. since there was a calculator there, i just inputted the values. back to the main question: the question asks the position. is the position in terms of what units? the angle and the y-displacement?

 

[Doc Al]

I assume that they want distance from the central maximum, which is the y-displacement.

 

[jairusgarcia]

ok thanks. last question. what is the physical explanation for the y-displacement? (sorry for this question. I am just confused)

 

[mgb_phys]

In simple terms it's the point on the screen where the difference in distance from each slit is 1 wavelength.
Here the two rays of light are in phase - the high points of the waves coincide - they add to give a maximum (bright point).
Where the difference is half a wavelength, the maxmum of one aligns with the minimum of another and they combine to give a minima (dark point)

 

[jairusgarcia]

thanks for all the help!