Answer:
40 cm
Explanation:
To find the distance between the third and first dark fringe you use the following formula:
[tex]y=(m+\frac{1}{2})\frac{\lambda D}{d}[/tex]
y: height of the dark fringe respect to the central peak
λ: wavelength of light
D: distance to the screen
d: distance between slits
Nexy, you calculate for m=3 and m= 1
[tex]y_3=(3+\frac{1}{2})\frac{(500*10^{-9}m)(8.0m)}{2.00*10^{-5}m}=0.7m\\\\y_1=(1+\frac{1}{2})\frac{(500*10^{-9}m)(8.0m)}{2.00*10^{-5}m}=0.3m[/tex]
Finally, you calculate the difference y3 - y1:
y3 - y1 = 0.7m - 0.3m = 0.4m = 40 cm
hence, the distance between the third ans first dark fringe is 40 cm
