To determine the distance between two adjacent bright fringes in an interference pattern created by a double-slit experiment, we can use the formula derived from Young's double-slit experiment. This formula relates the fringe spacing to the wavelength of the light, the distance between the slits, and the distance from the slits to the screen. Let's break this down step by step.
Understanding the Variables
In this scenario, we have the following information:
- Wavelength (λ): 589 nm (which is 589 x 10-9 m)
- Distance between the slits (d): 1.00 mm (which is 1.00 x 10-3 m)
- Distance to the screen (L): 225 cm (which is 2.25 m)
The Formula for Fringe Spacing
The distance between adjacent bright fringes (Δy) can be calculated using the formula:
Δy = (λ * L) / d
Where:
- Δy is the distance between adjacent bright fringes.
- 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 Values
Now, let's substitute the values into the formula:
λ = 589 x 10-9 m
L = 2.25 m
d = 1.00 x 10-3 m
Now, calculating Δy:
Δy = (589 x 10-9 m * 2.25 m) / (1.00 x 10-3 m)
Calculating the Result
First, calculate the numerator:
589 x 10-9 m * 2.25 m = 1.32425 x 10-6 m
Now, divide by the distance between the slits:
Δy = (1.32425 x 10-6 m) / (1.00 x 10-3 m) = 1.32425 x 10-3 m
Converting this to millimeters:
1.32425 x 10-3 m = 1.32425 mm
Final Answer
Rounding to two decimal places, the distance between two adjacent bright fringes is approximately 1.33 mm. Therefore, the correct answer is:
c. 1.33 mm
This calculation illustrates how the interference pattern is influenced by the wavelength of light and the geometry of the setup. The closer the slits are, or the longer the wavelength, the wider the spacing between the fringes will be. This experiment beautifully demonstrates the wave nature of light!
