Answer:
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:
[tex]y=\frac{\lambda (m+\frac{1}{2})D}{d}[/tex]
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
[tex]\lambda[/tex] is the wavelength of the light used
In this problem we have:
[tex]\lambda=683 nm = 683\cdot 10^{-9} m[/tex] is the wavelength of the light
[tex]d=1.1 mm = 0.0011 m[/tex] is the width of the slit
m = 13 is the order of the minimum
[tex]y=8.57 cm = 0.0857 m[/tex] 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:
[tex]D=\frac{yd}{\lambda(m+\frac{1}{2})}=\frac{(0.0857)(0.0011)}{(683\cdot 10^{-9})(13+\frac{1}{2})}=10.2 m[/tex]
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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