A light beam ( 557.1 nm) illustrates a single slit 0.85mm wide. (a) How far is the screen from the slit if there is 0.85 mm between the first minimum and the central minimum on the screen? (b) what is the width of the central maximum on the screen?
(a) b•sinφ = k•λ,
sinφ = k•λ/b = 1•557.1•10^9/0.85•10^-3 =
= 6.56•10^-4 = tan φ
tan φ = x/L ,
L = 0.85•10^-3/6.56•10^-4 = 1.3 m.
(b) 2•0.85 mm = 1.7 mm
To find the distance between the screen and the single slit, we can use the formula for the position of the first minimum in a single-slit diffraction pattern:
y_min = λ * L / (a * d),
where:
- y_min is the distance between the central minimum and the first minimum on the screen,
- λ is the wavelength of the light beam,
- L is the distance between the slit and the screen, which we need to find,
- a is the width of the single slit,
- d is the separation between the slit and the screen.
(a) To find L, we rearrange the formula:
L = (y_min * a * d) / λ.
Substituting the known values, we have:
y_min = 0.85 mm = 0.85 * 10^(-3) m,
a = 0.85 mm = 0.85 * 10^(-3) m,
d = ?
We need to determine the value of d, which is the separation between the slit and the screen. This information has not been given in the question, so we are unable to calculate the distance between the screen and the slit.
(b) To find the width of the central maximum on the screen, we can use the formula:
W = λ * L / a,
where:
- W is the width of the central maximum on the screen.
Again, we need the value of L (the distance between the slit and the screen) in order to calculate W. Since we do not have that information, we cannot determine the width of the central maximum.