Question

Two slits separated by 2.00 X 10(5 m are illuminated by light of wavelength 500nm. If the screen is 8.0 m from the slits, what is the distance between the m = 1 and m = 3 dark fringes?

Answer 1

40 cm

Step-by-step explanation:

To find the distance between the third and first dark fringe you use the following formula:

`y=(m+(1)/(2))(\lambda D)/(d)`

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

`y_3=(3+(1)/(2))((500*10^(-9)m)(8.0m))/(2.00*10^(-5)m)=0.7m\\\\y_1=(1+(1)/(2))((500*10^(-9)m)(8.0m))/(2.00*10^(-5)m)=0.3m`

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