Question

You are working in an optical research laboratory. Your supervisor needs you to set up a doubleslit apparatus for a presentation that will provide a vertically varying pattern of red light of wavelength 693 nm on a screen. The screen of width 4.75 m at the front of the presentation room must have red fringes on either end and 21 additional red fringes between those on the end. The separation between the slits in the double slit you will use at the back of the room is 65.0 µm.
You need to determine how far away from the slits (in m) the screen must be placed. (Assume the central maximum is at the center of the screen.)

Answer 1

Answer:

D = 10.31m

Explanation:

To find the screen distance you use the following formula:

$\Delta y=\frac{\lambda D}{d}\\\\D=\frac{d\Delta y}{\lambda}$  (1)

where delta y is the distance between fringes. You know the screen must have 21 fringes on each side of its center (plus the central one), that is:

$n_{fringes}=2*21+1=43\\\\\Delta y=\frac{4.75m}{43}=0.11m$

finally, by replacing the values of the parameters in (1) you obtain:

$D=\frac{(65*10^{-6}m)(0.11m)}{693*10^{-9}m}=10.31m$

hence, the distance to the screen is 10.31m