Central Maximum/Diffraction Question

[wilson_chem90]

a) A light with a wavelength of 500 nm illuminates two narrow slits that are 0.10 mm apart. If the viewing screen is 1.20 m from the slits, calculate the distance between each maxima.

b) How far would the fourth maximum be from the central maximum?


Relevant equations:
y1 = L x wavelength / w

The attempt at a solution:

a) y1 = L x wavelength / w
= (1.2m)(500 x 10^-9 m) / (1.0 x 10^-4 m)
= 0.006 m

0.006 m x 2 = 0.012 m

so the distance between each maximum is 1.2 x 10^-2 m

b) 4 x (1.2 x 10^-2 m)
= 0.048
= 4.8 x 10^-2 m

I'm not sure if this is correct, can someone please confirm or add any suggestions? thanks

 

[Delphi51]

It isn't perfectly clear what "distance between each maxima" is.
I would say it is the .006 m you found for the distance from the bright central maximum to the first order maximum. And I would multiply .006 by 4 to get part (b).

 

[tomcue]

.

Your calculations are correct. The distance between each maximum is 1.2 x 10^-2 m, and the fourth maximum would be located 4.8 x 10^-2 m from the central maximum. This is known as the fourth-order maximum. To confirm the accuracy of your calculations, you can also use the equation for the position of the nth maximum:

yn = n x L x wavelength / w

where n is the order of the maximum. Plugging in the values, we get:

y4 = 4 x (1.2m)(500 x 10^-9 m) / (1.0 x 10^-4 m) = 4.8 x 10^-2 m

This confirms that your calculations are correct. Keep in mind that these equations assume that the slits are very narrow compared to the wavelength of light, and that the light is monochromatic (single wavelength). If these assumptions are not met, the pattern of maxima and minima on the screen may be more complex.