Answer: a) the width is 2.54 mm
b) the angle is 0.012°
Explanation:
we have the equation:
λ = zw/(L*m)
Where is the distance for the middle of the screen, L is the distance to the screen, w is the widht of the slit and λ is the wavelength.
now we can isolate z and get:
z = λL*m/w
and the distance between the 5 minimum and the first one is 0.035mm
then:
0.035mm = λL*5/w - λL*1/w = λL*4/w
now we can solve it for w.
0.35mm = 570nm*39.0cm*4/w
now, we have all diferent units, lets use nanometers.
1cm = 1x10^-2 m
1mm = 1x10^-3 m
1nm = 1x10^-9m
then: 1 cm = 1x10^7 nm
1 mm = 1x10^6 nm
then we have:
0.35x10^6 nm = 570nm*39.0x10^7 nm*4/w
w = (570nm*39.0x10^7 nm*4)/0.35x10^6 nm =(570nm*39.0*10*4)/0.35
w = 2540571.4 nm
it is a bigg number, let's write it in milimeters:
w = (2540571.4/10^6) mm = 2.54 mm
the first minimum can be obtained by the equation w*sinθ = mλ by using m = 1
then we have:
2540571.4 nm*sinθ = 570 nm
sinθ = 570/2540571.4 = 0.000224
θ = asin(0.00022) = 0.012°
