To find the angular deviation of the third order bright fringe when monochromatic green light illuminates two parallel slits, we can use the formula derived from the double-slit interference pattern. The formula for the angular position of the bright fringes is given by:
Understanding the Formula
The angular position θ of the bright fringes is determined by the equation:
d sin(θ) = nλ
Here, d is the distance between the slits, n is the order of the fringe, and λ is the wavelength of the light.
Given Values
- Wavelength (λ): 554 nm = 554 x 10-9 m
- Distance between slits (d): 7.7 μm = 7.7 x 10-6 m
- Order of the fringe (n): 3
Calculating Angular Deviation
We can rearrange the formula to find sin(θ):
sin(θ) = nλ / d
Now, substituting the values:
sin(θ) = (3)(554 x 10-9 m) / (7.7 x 10-6 m)
Performing the Calculation
Calculating the right side:
sin(θ) = (1662 x 10-9) / (7.7 x 10-6)
Now, simplifying this gives:
sin(θ) = 0.216
Finding θ in Radians
To find θ, we take the inverse sine (arcsin) of 0.216:
θ = arcsin(0.216)
Using a calculator, we find:
θ ≈ 0.217 radians
Converting to Degrees
To convert radians to degrees, we use the conversion factor:
Degrees = Radians × (180/π)
Substituting our value:
Degrees ≈ 0.217 × (180/π) ≈ 12.43°
Final Results
Thus, the angular deviation of the third order bright fringe is:
- (a) in radians: 0.217 radians
- (b) in degrees: 12.43°
This calculation illustrates how light behaves in a double-slit experiment, demonstrating the wave nature of light through interference patterns. If you have any further questions or need clarification on any part of the process, feel free to ask!
