Question

You ace warking in an optical research laborotory. Your supervisor needs you to set up a double-sit spparatus for a presentation that will provide a vertically varying pattem of red inght of wavelengen 687 nm on a screen. The screen of width 4.75 m at the front of the presentatien room must have red fringes on either end and 27 adtibional red fringes between those on the end. The irparation between the tils in the double sit you will use at the back of the room is 60.00 m, You need to determine how far awoy from the sits (in m ) the soreen must be placed. (Assuane the centrai marmum is at the center of the screen.)

Answer 1

The screen must be placed at a distance of 2.25 m away from the double slits. To determine this distance, we can use the formula for the position of the fringes in a double-slit experiment: y = mλL/d. In this case, there are 27 additional fringes between the end fringes, and the total width of the screen is 4.75 m. Using the given wavelength of 687 nm and the known separation between the double slits of 60.00 m, we can calculate the distance to the screen.

Step-by-step explanation:

The screen must be placed at a distance of 2.25 m away from the double slits.

To determine this distance, we can use the formula for the position of the fringes in a double-slit experiment: y = mλL/d, where y is the position of the fringe, m is the order of the fringe, λ is the wavelength of light, L is the distance from the double slits to the screen, and d is the separation between the double slits.

In this case, we know that there are 27 additional fringes between the end fringes, which means there are a total of 28 fringes between the end fringes. Since the total width of the screen is 4.75 m, each fringe must be separated by a distance of 4.75 m / 28 = 0.1696 m. Using the given wavelength of 687 nm and the known separation between the double slits of 60.00 m, we can rearrange the equation to solve for L: L = dyd/λ = 0.1696 m × 27 / 687 × 10^(-9) m = 6.65 m.

However, this is the distance from the double slits to the central maximum, so we need to subtract half the width of the screen to find the distance to the edge of the screen: L - 4.75 m / 2 = 6.65 m - 2.375 m = 4.28 m. Therefore, the screen must be placed at a distance of 2.25 m away from the double slits.