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 in a single-slit diffraction pattern, you can use the equation y = λmL/a. Here's how to solve it:
a) Determine the linear size on the screen of the 2nd maximum (not including the central maximum):
- Given values:
- Wavelength (λ) = 600 nm = 600 x 10^-9 m
- Distance from the slit to the screen (L) = 2 m
- Width of the slit (a) = 2000 nm = 2000 x 10^-9 m
- m = 2 (since we want to find the 2nd maximum)
Plugging in these values into the equation, we get:
y = (600 x 10^-9 m) * (2) * (2 m) / (2000 x 10^-9 m)
y = 2.4 m
Therefore, the linear size on the screen of the 2nd maximum is 2.4 m (not 2.64 m as mentioned).
b) To determine the number of total maxima that occur in the pattern, you can use a formula: N = (2a/λ) * L, where N represents the total number of maxima. In this case, we want to find N.
- Given values:
- Wavelength (λ) = 600 nm = 600 x 10^-9 m
- Width of the slit (a) = 2000 nm = 2000 x 10^-9 m
- Distance from the slit to the screen (L) = 2 m
Applying these values to the formula, we have:
N = (2 * (2000 x 10^-9 m) / (600 x 10^-9 m)) * (2 m)
N = 6.67
Rounding to the nearest whole number, we have 7.
Therefore, the total number of maxima that occur in the pattern is approximately 7 (not 5 as mentioned).