A two-slit pattern is viewed on a screen 1.08 m from the slits. If the two fourth-order maxima are 52.8 cm apart, what is the total width of the central bright fringe?
To find the total width of the central bright fringe, we need to determine the distance between two consecutive bright fringes.
We can use the equation for fringe separation, which is given by:
Dλ/d = m
Where:
- D is the distance between the slits and the screen (1.08 m)
- λ is the wavelength of light
- d is the distance between the slits (unknown)
- m is the order of the bright fringe (4 in this case)
To solve for d, we rearrange the equation as follows:
d = Dλ/m
Substituting the given values, we have:
d = (1.08 m)(λ)/4
Now, let's find the value of λ (wavelength). For visible light, we can use an approximate value of 550 nm (nanometers) or 5.5 x 10^-7 m.
d = (1.08 m)(5.5 x 10^-7 m)/4
d ≈ 1.485 x 10^-7 m
The distance between two consecutive bright fringes (d) is approximately 1.485 x 10^-7 meters.
To find the total width of the central bright fringe, we multiply this distance by the number of bright fringes in between the fourth-order maxima.
In this case, the two fourth-order maxima are 52.8 cm apart, which is equal to 0.528 m.
Number of bright fringes between fourth-order maxima = (distance between maxima) / (distance between consecutive fringes)
Number of bright fringes = 0.528 m / 1.485 x 10^-7 m
Total width of central bright fringe = (number of bright fringes + 1) * distance between consecutive bright fringes
Total width of central bright fringe = (number of bright fringes + 1) * 1.485 x 10^-7 m
Now, you can substitute the calculated values above to find the total width of the central bright fringe.