A laser with wavelength d /8 is shining light on a double slit with slit separat

Question

A laser with wavelength d/8 is shining light on a double slit with slit separation 0.450mm . This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits.

What is the wavelength ?2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.450mm ?

I will choose best answer based on how detailed the explanation, I really need some help understanding this one. Thank you in adavance!

Explanation / Answer

The formulas to apply here are for maxima... y/L = m(wavelength)/d)

And for minima y/L = (m + .5)(wavelength)/d

y, L , and d are constants for the problem allowing us to set up a ratio...

m(wavelength)maxima = (m + .5)(wavelength)minima

(Note: For minima, m starts at zero, so the fourth minima has an m value of 3)

2(wavelength) = 3.5(4.5 X 10^-4/8)

wavelength = 9.84 X 10-5 m (which is d/4.57 in case you need it)

(NOTE: This is not in the visible spectrum, if this is not coming up as correct, please check what you typed in to the question. This answer is correct based on the information provided in the question. I used to teach Physics and can help further if needed. Please ask if you need to.)

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