Answer:
a) 1.8°
b) 0.18°
c) 0.018°
Explanation:
Wavelength (λ) = 630nm = 630 *10^-9m
The equation that describes the angular deflection of a dark band is
Wsin(βm) = mλ
w = width of the single slit
λ = wavelength of the light
βm = angular deflection of the mth dark band.
a) In order to get the angular deflection of the first dark band for a slit with 0.02mm width, substitute w = 0.02mm = 0.02*10^-3 , m = 1 , λ= 630*10^-9
0.02*10^-3 sin(β1) = 1 * 630*10^-9
Sin(β1) = 630 * 10^-9 / 0.02*10^-3
Sin(β1) = 0.0315
β1 = Sin^-1(0.0315)
= 1.8°
b) substitute w = 0.2mm = 0.2*10^-3 , m = 1 , λ= 630*10^-9
0.2*10^-3 sin(β1) = 1 * 630*10^-9
Sin(β1) = 630 * 10^-9 / 0.2*10^-3
Sin(β1) = 0.00315
β1 = Sin^-1(0.00315)
= 0.18°
c) substitute w = 2mm = 2*10^-3 , m = 1 , λ= 630*10^-9
2*10^-3 sin(β1) = 1 * 630*10^-9
Sin(β1) = 630 * 10^-9 / 2*10^-3
Sin(β1) = 3.15*10^-4
β1 = Sin^-1(3.15*10^-4)
= 0.018°
