•Coherent light with wavelength 400nm passes through two narrow slits that are separated by 0.2mm and the interference pattern is observed on a screen 4m from the slits.
–What is the width (in mm) of the central interference maximum?
The central interference maximum, also known as the central bright fringe, occurs at the center of the interference pattern. In this case, the central maximum corresponds to the point on the screen where the path difference between the two slits is zero.
The path difference (Δx) between the two slits can be calculated using the formula:
Δx = λ * L / d
Where:
- λ is the wavelength of the light (400nm = 400 x 10^-9 m)
- L is the distance between the slits and the screen (4m)
- d is the distance between the two slits (0.2mm = 0.2 x 10^-3 m)
Plugging in the values:
Δx = (400 x 10^-9) * (4) / (0.2 x 10^-3)
Δx = 8 x 10^-6 m
To find the width of the central interference maximum, take the path difference and divide it by the width per fringe. The width per fringe is given by:
width per fringe = λ * L / d
Plugging in the values:
width per fringe = (400 x 10^-9) * (4) / (0.2 x 10^-3)
width per fringe = 8 x 10^-6 m
Now divide the path difference by the width per fringe:
width of central interference maximum = Δx / (width per fringe)
width of central interference maximum = (8 x 10^-6) / (8 x 10^-6)
width of central interference maximum = 1 m
The width of the central interference maximum is 1 mm.
To find the width of the central interference maximum, we can use the formula for the interference pattern produced by two slits:
Width of interference maximum = (wavelength * distance to screen) / (separation of slits)
Given:
Wavelength (λ) = 400 nm = 400 * 10^6 mm
Separation of slits (d) = 0.2 mm
Distance to screen (L) = 4 m = 4000 mm
Using the formula, we can calculate the width of the central interference maximum:
Width = (λ * L) / d
= (400 * 10^6 * 4000) / 0.2
= 8 * 10^12 / 0.2
= 4 * 10^13 mm
Therefore, the width of the central interference maximum is 4 * 10^13 mm.