A single monochromatic indigo light source is shined through an etched, flat prism with a slit separation of .0250mm. the resulting interference pattern is viewed on a screen 1.25 m away. the third Maximum is found to be 6.6 cm from the central maximum.
What is the wavelength of the indigo light?
What are the first and second maxima?
Wow, that's quite a colorful question! Alright, let's shed some light on it, shall we?
To find the wavelength of the indigo light, we can use the formula for the separation of maxima in a double-slit interference pattern:
Δy = (λL) / d
Where:
Δy is the separation between maxima (in this case, it's the distance from the third maximum to the central maximum, which is 6.6 cm or 0.066 m),
λ is the wavelength we're trying to find,
L is the distance between the screen and the prism (1.25 m), and
d is the slit separation (0.0250 mm or 0.000025 m).
Plugging in the numbers, we get:
0.066 = (λ × 1.25) / 0.000025
Simplifying that, we find:
λ ≈ 0.0000165 meters
So, the wavelength of the indigo light is approximately 0.0000165 meters.
Now, let's move on to the first and second maxima. In a double-slit interference pattern, the central maximum is at the center, and the first maximum occurs on either side of it. The distance from the first maximum to the central maximum can be found using the formula:
Δy = (λL) / d
Since we already know the values of λ, L, and d, we can plug them in to find:
Δy = (0.0000165 × 1.25) / 0.000025
Simplifying that, we get:
Δy ≈ 0.0825 meters
So, the distance from the central maximum to the first maximum is approximately 0.0825 meters. Since the first maximum occurs on either side of the central maximum, the first maximum itself would be at a distance of half of that, which is approximately 0.04125 meters.
The second maximum would be at twice the distance from the central maximum, so it would be approximately 0.0825 meters.
So, the first maximum is about 0.04125 meters from the central maximum, and the second maximum is about 0.0825 meters from the central maximum.
Hope that brightened up your day!
To find the wavelength of the indigo light, we can use the formula for the slit separation in Young's double-slit experiment:
λ = (d * x) / L
where:
λ = wavelength of light
d = slit separation
x = distance from central maximum to desired maximum
L = distance from the slits to the screen
Given:
Slit separation (d) = 0.0250 mm = 0.0250 * 10^(-3) m
Distance from the central maximum to the third maximum (x) = 6.6 cm = 6.6 * 10^(-2) m
Distance from the slits to the screen (L) = 1.25 m
Let's substitute these values into the formula to find the wavelength:
λ = (0.0250 * 10^(-3) m * 6.6 * 10^(-2) m) / 1.25 m
Calculating this expression:
λ = (0.00165 * 10^(-5)) / 1.25
= 1.32 * 10^(-9) m
Therefore, the wavelength of the indigo light is approximately 1.32 * 10^(-9) m.
To find the first and second maxima, we can use the formula for the position of the nth maximum in Young's double-slit experiment:
x_n = (n * λ * L) / d
where:
x_n = position of the nth maximum
n = order of the maximum (1 for the first maximum, 2 for the second maximum, and so on)
λ = wavelength of light
L = distance from the slits to the screen
d = slit separation
Given:
wavelength of light (λ) = 1.32 * 10^(-9) m
slit separation (d) = 0.0250 * 10^(-3) m
distance from the slits to the screen (L) = 1.25 m
Let's substitute these values into the formula to find the positions of the first and second maxima:
For the first maximum (n = 1):
x_1 = (1 * 1.32 * 10^(-9) m * 1.25 m) / (0.0250 * 10^(-3) m)
Calculating this expression:
x_1 = (1.65 * 10^(-9)) / (2.5 * 10^(-5))
= 6.6 * 10^(-5) m = 6.6 cm
Therefore, the first maximum is located 6.6 cm from the central maximum.
For the second maximum (n = 2):
x_2 = (2 * 1.32 * 10^(-9) m * 1.25 m) / (0.0250 * 10^(-3) m)
Calculating this expression:
x_2 = (3.30 * 10^(-9)) / (2.5 * 10^(-5))
= 13.2 * 10^(-5) m = 13.2 cm
Therefore, the second maximum is located 13.2 cm from the central maximum.
To find the wavelength of the indigo light, we can use the formula for the interference pattern produced by a double-slit setup:
λ = (d * x) / L
Where:
λ is the wavelength of the light
d is the separation between the slits (also known as the slit separation)
x is the distance from the central maximum to the nth maximum (in this case, the third maximum)
L is the distance from the double slit to the screen.
From the given information:
Slit separation (d) = 0.0250 mm = 0.0250 × 10^(-3) m
Distance to the screen (L) = 1.25 m
Distance from the central maximum to the third maximum (x) = 6.6 cm = 6.6 × 10^(-2) m
Now, we can substitute these values into the formula to find the wavelength (λ):
λ = (0.0250 × 10^(-3) m * 6.6 × 10^(-2) m) / 1.25 m
Calculating this expression will give us the wavelength of the indigo light.
To find the positions of the first and second maxima, we can use the formula for the position of the interference maxima:
Y = m * λ * L / d
Where:
Y is the distance from the central maximum to the mth maximum
m is the order of the maximum (1 for the first, 2 for the second, and so on)
We can substitute the known values into this formula to find the positions of the first and second maxima.