two slits are spaced0.3mm apart and are placed 50cm from ascreen what is the distance b/n 2nd and 3rd dark pattern when alight of 6oonm
To find the distance between the 2nd and 3rd dark pattern on a screen, we need to use the concept of interference in double-slit experiments.
First, we need to calculate the distance between adjacent bright fringes, known as the fringe spacing. This can be found using the formula:
d = λL / D
Where:
- d is the fringe spacing
- λ is the wavelength of light
- L is the distance from the slits to the screen
- D is the distance between the slits
Given the values:
- λ (wavelength) = 600 nm (0.6 μm)
- L (distance from slits to screen) = 50 cm (0.5 m)
- D (distance between slits) = 0.3 mm (0.0003 m)
Plugging the values into the formula:
d = (0.6 μm) * (0.5 m) / (0.0003 m)
d ≈ 1 mm
So, the fringe spacing is approximately 1 mm.
Now, we can calculate the distance between the 2nd and 3rd dark pattern. In a double-slit experiment, the dark fringes are located halfway between the bright fringes. Therefore, the distance between the dark fringes is equal to half the fringe spacing:
Distance between 2nd and 3rd dark pattern = (1 mm) / 2
Distance between 2nd and 3rd dark pattern = 0.5 mm
Therefore, the distance between the 2nd and 3rd dark pattern is approximately 0.5 mm.