1. A pair of narrow, parallel slits separated by a distance of 0.408 mm are illuminated by green laser light with wavelength of λ = 537.5 nm. The interference pattern is observed on a screen 1.56 m from the plane of the parallel slits. Calculate the distance from the central maximum to the first bright region on either side of the central maximum.
2. What is the distance between the first and second dark bands in the interference pattern?
To answer both questions, we need to use the concept of interference and the formula for calculating the position of bright and dark regions in the interference pattern.
Interference occurs when two or more waves overlap or combine with each other. In this case, when the laser light passes through the two narrow, parallel slits, it creates two coherent sources of light that interfere with each other.
1. To calculate the distance from the central maximum to the first bright region on either side of the central maximum, we can use the formula:
y = (λ * L) / d,
where:
y is the distance from the central maximum to the bright region,
λ is the wavelength of the light,
L is the distance between the slits and the screen, and
d is the distance between the slits.
Given:
λ = 537.5 nm = 537.5 × 10^(-9) m (convert from nanometers to meters)
L = 1.56 m
d = 0.408 mm = 0.408 × 10^(-3) m (convert from millimeters to meters)
Substituting the given values into the formula, we have:
y = (537.5 × 10^(-9) m * 1.56 m) / (0.408 × 10^(-3) m)
Calculating the above expression gives us the value of y, which represents the distance from the central maximum to the first bright region on either side.
2. To find the distance between the first and second dark bands, we can use the formula:
y = (λ * L) / (2 * d),
where the variables have the same meanings as in the previous question.
Substituting the given values into the formula, we have:
y = (537.5 × 10^(-9) m * 1.56 m) / (2 * 0.408 × 10^(-3) m)
Calculating the above expression gives us the value of y, which represents the distance between the first and second dark bands.
By performing these calculations, you will obtain the answers to the two questions.
1. To calculate the distance from the central maximum to the first bright region on either side of the central maximum, we can use the formula:
y = (λ * L) / d
Where:
y is the distance from the central maximum to the first bright region,
λ is the wavelength of the light,
L is the distance from the slits to the screen,
d is the distance between the slits.
Plugging in the given values:
λ = 537.5 nm = 5.375 × 10^-7 m
L = 1.56 m
d = 0.408 mm = 4.08 × 10^-4 m
y = ((5.375 × 10^-7) * (1.56)) / (4.08 × 10^-4)
y ≈ 0.00205 m
Therefore, the distance from the central maximum to the first bright region on either side of the central maximum is approximately 0.00205 m.
2. To calculate the distance between the first and second dark bands in the interference pattern, we can use the formula:
Δy = λ * L / d
Where:
Δy is the distance between adjacent dark bands,
λ is the wavelength of the light,
L is the distance from the slits to the screen,
d is the distance between the slits.
Plugging in the given values:
λ = 537.5 nm = 5.375 × 10^-7 m
L = 1.56 m
d = 0.408 mm = 4.08 × 10^-4 m
Δy = (5.375 × 10^-7 * 1.56) / (4.08 × 10^-4)
Δy ≈ 0.00206 m
Therefore, the distance between the first and second dark bands in the interference pattern is approximately 0.00206 m.