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?
Ans: laser 1

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

    
      Δ_ymax-max= ______ m

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

    
     Δ_ymax-min = ______ m

Answer 1

For part be we can use the equation

y_{m =} m*λ*L/d

so for the first max for each one m =1

so for laser 1

y = (d/20)*(6.0m)/d

the d cancel out so we have

y = 6.0m /20 = 0.3
for laser 2 we do the same thing

y = 6.0m/15 = 0.4
y ( laser1 )   <   y ( laser2 )

(1) hence   first maxima of laser1 is closest to central maxima
Δy = 0.4m -0 .3 m = 0.1m

For part C)

we use the same equation to find the y for laser 1, except m =2

y= 2*6.0 m / 20   = 0.6 m

Now for laser 2 we use:

y_m=(m+1/2)*λ*L/d

since there is no central minimum the first minimum is at m = 0.that means that the third minimum is at m = 2
simplifying the equation we get
y = (2.5)*6.0 / 15 =   1m  

now we solve
Δy=     1m   -   0.6m   = 0.4 m