How Far is the Third Interference Minimum in a Double Slit Experiment?

[wahsup13]

Homework Statement

Light of wavelength = 655 nm passes through a pair of slits that are 245 µm apart and travels to a screen 9.0 m away. How far from the center of the pattern is the third interference minimum? (in mm)

d=245e-6
λ=655e-9
m=3
D=9
y=distance from center of 3rd interference minimum

Homework Equations

sinθ=λm/d
tanθ=y/D

The Attempt at a Solution

sinθ=λm/d=(655e-9)(3)/(245e-6)
θ=0.4595 degrees

tanθ=y/D
y=Dtanθ=9tan(0.4595)
y=0.722m=72.2mm (incorrect)

 

[Delphi51]

Hi Wahsup, welcome to PF!
It seems to me you have found the 3rd maximum, but the question asks for the MINIMUM. You'll just have to adjust your m value.

 

[wahsup13]

Hi Wahsup, welcome to PF!
It seems to me you have found the 3rd maximum, but the question asks for the MINIMUM. You'll just have to adjust your m value.

thanks!

if m=3 is the max, would that mean m=2 is the min?

 

[wahsup13]

nevermind. i got it.

Since m=3 is the max, the min is m=2.5

thank you for the help