Using a 683 nm wavelength laser, you form the diffraction pattern of a 1.1 mm wide slit on a screen. You measure on the screen that the 13 th dark fringe is 8.57 cm away from the center of the central maximum. How far is the screen located from the slit

The distance at which the screen is far from the slit is; D = 10.22 m

We are given;

Wavelength; λ = 683 nm = 683 × 10^(-9) m

Diffraction pattern; d = 1.1 mm = 0.0011 m

Position of 13th dark fringe; y = 8.57 cm = 0.0857 m

Order of minimum; m = 13

Now,formula to get the distance of slit from the screen is;

D = yd/(λ(m + ½)

Plug in the relevant values to get;

D = (0.0857 × 0.0011)/(683 × 10^(-9) × (13 + ½))

D = 10.22 m

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10.2 m

Explanation:

The position of the dark fringes (destructive interference) formed on a distant screen in the interference pattern produced by diffraction from a single slit are given by the formula:

where

y is the position of the m-th minimum

m is the order of the minimum

D is the distance of the screen from the slit

d is the width of the slit

is the wavelength of the light used

In this problem we have:

is the wavelength of the light

is the width of the slit

m = 13 is the order of the minimum

is the distance of the 13th dark fringe from the central maximum

Solving for D, we find the distance of the screen from the slit: