The pattern of bright and dark bands, known as fringes, observed when light is shone through a double slit is a result of the interference of light waves.
When light passes through the double slit, it splits into two coherent wavefronts, each originating from one of the slits. These two wavefronts then overlap and interfere with each other.
Interference occurs when two waves meet and combine. If the peaks (or crests) of the two waves coincide, they interfere constructively and result in a bright fringe. On the other hand, if the peak of one wave coincides with the trough (or valley) of the other wave, they interfere destructively and result in a dark fringe.
The interference pattern is a consequence of the superposition of these waves after passing through the double slit. When the path difference between the two waves is an integral multiple of the wavelength of light, the waves interfere constructively and form bright fringes, creating regions of maximum intensity known as maxima. Conversely, when the path difference is a half integral multiple of the wavelength, the waves interfere destructively and form dark fringes, creating regions of minimum or zero intensity known as minima.
The pattern of bright and dark fringes depends on various factors, such as the wavelength of light, the distance between the slits (known as slit separation), and the distance between the double slit and the screen (known as the screen distance). The spacing between the fringes becomes closer as the wavelength of light decreases or the slit separation increases.
Therefore, the observed interference pattern in a double-slit experiment is a result of the wave nature of light and the constructive and destructive interference of the waves produced by the two slits.
When light is shone through a double slit, a pattern of bright and dark bands, fringes are visible on a screen. Using your knowledge of light properties, explain why this pattern occurs.
5 answers
Upon using Thomas Young’s double-slit experiment to obtain measurements, the following data were obtained. Use these data to determine the wavelength of light being used to create the interference pattern. Do this using three different methods.
To determine the wavelength of light using Thomas Young's double-slit experiment, three methods can be employed: using the fringe separation formula, using the grating equation, and using the path difference formula. Here's how each method works:
Method 1: Fringe Separation Formula
In this method, we use the formula:
λ = (d * sinθ) / m
Where:
λ = wavelength of light
d = distance between the double slits (known as the slit separation)
θ = angle from the central maximum to the mth fringe (measured from the center of the central peak)
m = order of the fringe (0 for the central maximum, ±1 for the first-order, ±2 for the second-order, and so on)
The fringe separation formula relates the wavelength of light to the distance between the slits, the angle from the central maximum to a fringe, and the order of the fringe.
Method 2: Grating Equation
The grating equation is similar to the fringe separation formula, but it is specifically used when a diffraction grating is employed instead of a double slit. The formula is:
λ = d * sinθ / m
Where:
λ = wavelength of light
d = spacing between the lines of the diffraction grating
θ = angle from the normal to the mth order fringe (measured from the normal to the grating)
m = order of the fringe
If a diffraction grating is used in place of a double slit and you have the relevant data, you can use this equation to determine the wavelength of light.
Method 3: Path Difference Formula
The path difference formula is another method for determining the wavelength of light:
λ = (d * y) / D
Where:
λ = wavelength of light
d = distance between the double slits
y = distance from the central maximum to the mth fringe on the screen
D = distance from the double slit to the screen
Using the given measurements, such as the distance between the double slits, the distance to the screen, and the position of fringes, you can apply the path difference formula to calculate the wavelength of light.
To determine the actual wavelength of light using these methods, it is necessary to have the measurements taken during the experiment and substitute them into the corresponding formulas. Unfortunately, since the data obtained from the experiment were not provided in the question, it is not possible to perform the calculations for the three different methods.
Method 1: Fringe Separation Formula
In this method, we use the formula:
λ = (d * sinθ) / m
Where:
λ = wavelength of light
d = distance between the double slits (known as the slit separation)
θ = angle from the central maximum to the mth fringe (measured from the center of the central peak)
m = order of the fringe (0 for the central maximum, ±1 for the first-order, ±2 for the second-order, and so on)
The fringe separation formula relates the wavelength of light to the distance between the slits, the angle from the central maximum to a fringe, and the order of the fringe.
Method 2: Grating Equation
The grating equation is similar to the fringe separation formula, but it is specifically used when a diffraction grating is employed instead of a double slit. The formula is:
λ = d * sinθ / m
Where:
λ = wavelength of light
d = spacing between the lines of the diffraction grating
θ = angle from the normal to the mth order fringe (measured from the normal to the grating)
m = order of the fringe
If a diffraction grating is used in place of a double slit and you have the relevant data, you can use this equation to determine the wavelength of light.
Method 3: Path Difference Formula
The path difference formula is another method for determining the wavelength of light:
λ = (d * y) / D
Where:
λ = wavelength of light
d = distance between the double slits
y = distance from the central maximum to the mth fringe on the screen
D = distance from the double slit to the screen
Using the given measurements, such as the distance between the double slits, the distance to the screen, and the position of fringes, you can apply the path difference formula to calculate the wavelength of light.
To determine the actual wavelength of light using these methods, it is necessary to have the measurements taken during the experiment and substitute them into the corresponding formulas. Unfortunately, since the data obtained from the experiment were not provided in the question, it is not possible to perform the calculations for the three different methods.
Upon using Thomas Young’s double-slit experiment to obtain measurements, the following data were obtained. Use these data to determine the wavelength of light being used to create the interference pattern. Do this using three different methods.
The angle to the eighth maximum is 1.12°.
The distance from the slits to the screen is 302.0 cm.
The distance from the central maximum to the fifth minimum is 3.33 cm.
The distance between the slits is 0.000250 m.
The angle to the eighth maximum is 1.12°.
The distance from the slits to the screen is 302.0 cm.
The distance from the central maximum to the fifth minimum is 3.33 cm.
The distance between the slits is 0.000250 m.
Using the provided data, we can now calculate the wavelength of light using three different methods: the fringe separation formula, the grating equation, and the path difference formula.
Method 1: Fringe Separation Formula
We can use the formula λ = (d * sinθ) / m, where λ is the wavelength, d is the distance between the double slits, θ is the angle from the central maximum to the mth fringe, and m is the order of the fringe.
Using the given angle to the eighth maximum θ = 1.12° and the slit separation d = 0.000250 m (or 2.50 x 10^-4 m), we can calculate the wavelength λ.
θ = 1.12° = 0.01955 radians (since 1° = π/180 radians)
For the eighth maximum, m = 8
λ = (d * sinθ) / m
= (2.50 x 10^-4 m) * sin(0.01955) / 8
Calculating this expression will give us the value of λ.
Method 2: Grating Equation
Since the provided data does not mention the use of a diffraction grating, we cannot apply this method in this case. Thus, we will skip this method.
Method 3: Path Difference Formula
We can use the formula λ = (d * y) / D, where λ is the wavelength, d is the distance between the double slits, y is the distance from the central maximum to the mth fringe on the screen, and D is the distance from the double slit to the screen.
Using the given distance from the central maximum to the fifth minimum y = 3.33 cm (or 0.0333 m), the slit separation d = 0.000250 m (or 2.50 x 10^-4 m), and the distance from the double slit to the screen D = 302.0 cm (or 3.02 m), we can calculate the wavelength λ.
λ = (d * y) / D
= (2.50 x 10^-4 m) * (0.0333 m) / (3.02 m)
Calculating this expression will give us the value of λ.
By substituting the given measurements into the appropriate formulas, we can calculate the wavelength of light using the fringe separation formula and the path difference formula.
Method 1: Fringe Separation Formula
We can use the formula λ = (d * sinθ) / m, where λ is the wavelength, d is the distance between the double slits, θ is the angle from the central maximum to the mth fringe, and m is the order of the fringe.
Using the given angle to the eighth maximum θ = 1.12° and the slit separation d = 0.000250 m (or 2.50 x 10^-4 m), we can calculate the wavelength λ.
θ = 1.12° = 0.01955 radians (since 1° = π/180 radians)
For the eighth maximum, m = 8
λ = (d * sinθ) / m
= (2.50 x 10^-4 m) * sin(0.01955) / 8
Calculating this expression will give us the value of λ.
Method 2: Grating Equation
Since the provided data does not mention the use of a diffraction grating, we cannot apply this method in this case. Thus, we will skip this method.
Method 3: Path Difference Formula
We can use the formula λ = (d * y) / D, where λ is the wavelength, d is the distance between the double slits, y is the distance from the central maximum to the mth fringe on the screen, and D is the distance from the double slit to the screen.
Using the given distance from the central maximum to the fifth minimum y = 3.33 cm (or 0.0333 m), the slit separation d = 0.000250 m (or 2.50 x 10^-4 m), and the distance from the double slit to the screen D = 302.0 cm (or 3.02 m), we can calculate the wavelength λ.
λ = (d * y) / D
= (2.50 x 10^-4 m) * (0.0333 m) / (3.02 m)
Calculating this expression will give us the value of λ.
By substituting the given measurements into the appropriate formulas, we can calculate the wavelength of light using the fringe separation formula and the path difference formula.