Two slits are 0.158 mm apart. A mixture of red light ( wavelength = 65 nm) and yellow green light (wavelength = 565 nm)falls on the slits. A flat observation screen is located 2.24 m away. What's the distance on the screen between the third order red fringe and the third order yellow green fringe?
To find the distance between the third-order red fringe and the third-order yellow-green fringe on the observation screen, we need to consider the concept of interference patterns formed by the double-slit experiment. Here's how you can calculate it:
1. Determine the separation between the slits (d):
The given information states that the slits are 0.158 mm apart. However, for further calculations, we need this value in meters, so we convert it:
d = 0.158 mm = 0.158 × 10^(-3) m
Therefore, the separation between the slits (d) is 0.158 × 10^(-3) m.
2. Determine the wavelengths of the lights (λ1 and λ2):
The red light has a wavelength of 65 nm, which we convert to meters by dividing by 10^9:
λ1 = 65 nm = 65 × 10^(-9) m
The yellow-green light has a wavelength of 565 nm, which we convert to meters similarly:
λ2 = 565 nm = 565 × 10^(-9) m
3. Calculate the distances to each fringe for the given order (m):
The distance to each fringe (y) for the mth order can be determined using the formula:
y = (m * λ * L) / d
Where:
y = distance to the fringe
m = order of the fringe
λ = wavelength of light
L = distance between the slits and the screen
d = separation between the slits
4. Calculate the distances to the third-order red and yellow-green fringes:
We are interested in the third-order red and yellow-green fringes, so we calculate the distances to these fringes using the given values:
For the red light (λ1 = 65 × 10^(-9) m) fringe:
y1 = (3 * 65 × 10^(-9) * 2.24) / (0.158 × 10^(-3))
For the yellow-green light (λ2 = 565 × 10^(-9) m) fringe:
y2 = (3 * 565 × 10^(-9) * 2.24) / (0.158 × 10^(-3))
5. Calculate the distance between the third-order red and yellow-green fringes:
The distance between the third-order red and yellow-green fringes (Δy) can be calculated as:
Δy = |y1 - y2|
Calculate the absolute difference between the distances obtained in the previous step to find the desired distance.
Now you can apply these calculations to find the answer.
To find the distance on the screen between the third order red fringe and the third order yellow green fringe, we can use the equation for the fringe separation:
Δy = (λ * L) / d
where:
Δy is the fringe separation
λ is the wavelength of light
L is the distance between the slits and the observation screen
d is the distance between the slits
Let's calculate the fringe separation for both the red light and yellow-green light, and then find the difference between them.
For the third-order fringe:
For red light:
λRed = 65 nm = 65 * 10^(-9) m
L = 2.24 m
d = 0.158 mm = 0.158 * 10^(-3) m
ΔyRed = (λRed * L) / d
For yellow-green light:
λYellowGreen = 565 nm = 565 * 10^(-9) m
L = 2.24 m
d = 0.158 mm = 0.158 * 10^(-3) m
ΔyYellowGreen = (λYellowGreen * L) / d
Now, let's substitute the values and calculate the values for Δy.
For red light:
ΔyRed = (65 * 10^(-9) * 2.24) / (0.158 * 10^(-3)) = 0.92 m
For yellow-green light:
ΔyYellowGreen = (565 * 10^(-9) * 2.24) / (0.158 * 10^(-3)) = 12.72 m
Finally, we can find the difference between the two values of Δy:
ΔyDifference = |ΔyYellowGreen - ΔyRed| = |12.72 - 0.92| = 11.8 m
Therefore, the distance on the screen between the third order red fringe and the third order yellow green fringe is 11.8 meters.
take each wavelength: calcute the distance from center for each wavelength at that order.
then subtract. http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html