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

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 6.00 m away from the slits.
Which laser has its first maximum closer to the central maximum?
What is the distance between the first maxima (on the same side of the central maximum) of the two patterns?
What is the distance between the second maximum of laser 1 and the third minimum of laser 2, on the same side of the central maximum?

Explanation / Answer

use the formula d sin = m

given 1=d/20

sin 1 = m/20................(1)

given 2=d/15

sin 2 = m/15

also height of maximum h= D.

now sin 2 > sin 1

so h1 < h2

Hence laser 1 has closer maxima.

(b) Difference between first maxima of both lasers = D(2-1)

also for first maxima m = 1

and D = 5.00m

use sin if is very small

Difference between first maxima of both lasers = 5 (1/15 - 1/20) = 0.084 m

(c)  Difference between second maxima of laser 1 and third minimum of laser 2

for minima

d sin = (m+1/2)

put 2=d/15

for third minimum put m=3

sin 2 = (3+1/2)/15

= 0.24

for second maxima of laser 1 from eqn.1

sin 1 = 2/20=0.1

Difference between second maxima of laser 1 and third minimum of laser 2 = 5 (0.24-0.1) = 0.67 m

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