Answer:
a) 0.063m
b) 2.72°
c) 3151 fringes
d) 1.87*10^-6m
Explanation:
a) To find the screen distance you use the following formula:
[tex]y=\frac{m\lambda D}{d}\\\\D=\frac{dy}{m\lambda}[/tex]
D: screen distance
d: distance between slits
m: order of the fringes
λ: wavelength
By replacing the values of the parameters you obtain:
[tex]D=\frac{(0.02*10^{-3}m)(0.2*10^{-2}m)}{(1)(633*10^{-9}m)}=0.063m[/tex]
b) The condition for dark fringes is given by:
[tex]\lambda(m+\frac{1}{2})=dsin\theta[/tex]
for the first dark fringe the angle is:
[tex]\theta=sin^{-1}(\frac{\lambda(m+\frac{1}{2})}{d})\\\\\theta=sin^{-1}(\frac{(633*10^{-9}m)(1+\frac{1}{2})}{0.02*10^{-3}m})=2.72\°[/tex]
c) the visible number of fringes is given by:
[tex]N=1+2\frac{D}{d}=1+\frac{0.063m}{0.02*10^{-3}}=3151 \ fringes[/tex]
d) the wavelength of a laser in which its first order fringe coincides with the third one of the CuAr laser is:
[tex]y=\frac{(3)(633*10^{-9}m)(0.063m)}{0.02*10^{-3}m}=5.98*10^{-3}m\approx0.59cm\\\\\lambda'=\frac{dy}{mD}=\frac{(0.02*10^{-3}m)(0.59*10^{-2}m)}{(1)(0.063m)}=1.87*10^{-6}m[/tex]
