Light Interference: Slit Separation & Maxima Observation

[matpo39]

im a little stuck on part b of this question.


Light of wavelength 633 nm from a helium-neon laser is shone normally on a plane containing two slits. The first interference maximum is 85 cm from the central maximum on a projection screen 14 m away.

(a) Find the separation of the slits.

(b) How many interference maxima (including the central maximum) can be observed, assuming your projection screen can be as large as you want?

i was able to get part a by using the small angle formula y=(R*m*x)/d
where y= the maxima seperation, R=the distance to the screen, x=the wave length, d=the slit separation and in the case for part a m=1
i found d to be 10.4 micro meters which turned out right. now for part b) my initial reaction was that since the screen is infinit and that m=+-1,+-2... and since the wave length is fixed at 633 nm that there would be infinite maxima points.

can anyone verify this for me since i am unsure if this is correct.
thanks

 

[Pseudopod]

I'm not sure if that's correct - it could be. The way I would go about solving part b would be to find an equation relating the angle $$\theta$$ (as viewed from the slit's perspective, $$\theta$$ would be the angle between the middle maxima and any given "mth" maxima) to the integer number m of the maxima you are looking at. You could then plug in $$\theta=90$$ and solve for the mth maxima.

 

[wais]

Your initial reaction is correct. Since the projection screen can be as large as you want and the wavelength is fixed, there will be an infinite number of interference maxima observed. This is because as the screen size increases, the number of maxima will also increase as the distance between them becomes smaller. Additionally, the formula for calculating the number of maxima is n = (d/λ) * m, where n is the number of maxima, d is the slit separation, λ is the wavelength, and m is the order of the maxima (1, 2, 3...). Since the screen size is infinite, the number of maxima will also be infinite. Therefore, your answer for part b is correct.