Two lasers are shining on a double slit, with slit separation d . Laser 1 has a

Question

Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 5.20m away from the slits.

A)What is the distance ?ymax?max between the first maxima (on the same side of the central maximum) of the two patterns?

B)What is the distance ?ymax?min between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

Explanation / Answer

this equation will closely approximate this situation

n? / d = y / l
n is the order of image (1,2,3;;;)
? is wavelength
y is distance of image from center point of screen
l is distance of slits from screen

this equation assumes either that the screen is curved and y is measured as a chord
or
that the angle between central image and other images is small enough that sin? is essentially equal to tan?

solve for the image distance from center (y) then take the difference to get the distance between them

having ? as a fraction of d makes the math simple
1*(d/20) / d = y / 5.6, y = 28 cm
1*(d/15) / d = y / 5.6, y = 37.3 cm
so the distance between them is 9.3 cm

you may wish to draw it out and use sin? = n? / d and tan? = y / l
this will give essentially the same answer for first order images but may differ a little bit with the third order image
your call.

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