Orange light (wavelength=600nm) is passes through a single slit. Use a=2000nm and L=2m.
a) Determine the linear size on the screen of the 2nd maximum (not including the central maximum).
b) Determine how many total maxima occur in the pattern.
a) I thought for a single slit, the equation would be y=WL*m*L/a, but my answer comes out incorrect. The answer is 2.64m
b) I have no idea but the answer is 5.
To determine the linear size on the screen of the 2nd maximum (not including the central maximum), you can use the formula for the position of the maxima in a single slit diffraction pattern:
y = (m * λ * L) / a
where:
y is the distance on the screen from the central maximum to the m-th maximum,
m is the order of the maximum (m = 0 for the central maximum),
λ is the wavelength of the light,
L is the distance between the slit and the screen, and
a is the width of the slit.
In this case, you are looking for the 2nd maximum, so m = 2. The wavelength of the orange light is given as 600 nm, which is equal to 600 * 10^-9 meters. The distance between the slit and the screen is L = 2 meters, and the width of the slit is a = 2000 nm, which is equal to 2000 * 10^-9 meters.
Plugging these values into the formula, we have:
y = (2 * 600 * 10^-9 meters * 2 meters) / (2000 * 10^-9 meters)
= (1.2 * 10^-6 meters * 2) / (2 * 10^-6 meters)
= 1.2 * 2
= 2.4 meters
Therefore, the linear size on the screen of the 2nd maximum is 2.4 meters.
Now, to determine the number of total maxima that occur in the pattern, we can use the formula:
N = (2 * a) / λ
where N is the total number of maxima, a is the width of the slit, and λ is the wavelength of the light.
In this case, plugging in the values, we have:
N = (2 * 2000 * 10^-9 meters) / (600 * 10^-9 meters)
= (4000 * 10^-9 meters) / (600 * 10^-9 meters)
= 4000 / 600
≈ 6.67
Since we're dealing with interference, the number of maxima cannot be a decimal and must be a whole number. Therefore, the closest whole number to 6.67 is 7.
However, since we are excluding the central maximum, we subtract 1 from the total number of maxima.
Therefore, the total number of maxima in this pattern is 7 - 1 = 6.
So, the correct answers are:
a) The linear size on the screen of the 2nd maximum is 2.4 meters.
b) The total number of maxima in the pattern (excluding the central maximum) is 6.