At most, how many bright fringes can be formed on either side of the central bright fringe when light of wavelength 656 nm falls on a double slit whose slit separation is 3.45 × 10-6 m?

Pick the order m that has a diffraction angle of 90 degrees.

Use the formula at
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html#c1

Then double the order number, since there are fringes on both sides of the central bright fringe.

To find the maximum number of bright fringes on either side of the central bright fringe, we can use the formula for the number of bright fringes in a double-slit interference pattern:

n = (2d sinθ) / λ

where:
n is the number of bright fringes,
d is the slit separation,
θ is the angle between the central maximum and the nth bright fringe,
and λ is the wavelength of light.

Given:
d = 3.45 × 10^(-6) m (slit separation)
λ = 656 nm = 656 × 10^(-9) m (wavelength of light)

To find the maximum number of bright fringes, we need to find the largest value of n. This occurs when sinθ is equal to 1, which corresponds to the first bright fringe.

Plugging in the values into the formula:

n = (2d sinθ) / λ
n = (2 × 3.45 × 10^(-6) m × 1) / (656 × 10^(-9) m)
n = (6.9 × 10^(-6) m) / (656 × 10^(-9) m)
n = 10.52

Since we can only have whole-number values for n, the maximum number of bright fringes on either side of the central bright fringe is 10 on each side. Therefore, a total of 21 bright fringes can be formed on either side of the central bright fringe.

To determine the maximum number of bright fringes formed on either side of the central bright fringe, we need to use the formula for the number of bright fringes in a double-slit interference pattern. The formula is given by:

n = (L * λ) / d

Where:
n = number of bright fringes
L = distance between the double-slit and the screen
λ = wavelength of light
d = slit separation

In this case, we are given the following values:
λ = 656 nm = 656 × 10^(-9) m
d = 3.45 × 10^(-6) m

The distance L is not provided in the question. However, we can assume a standard experiment setup where the double-slit is placed at a distance much larger than the separation between the slits.

In such a setup, the central bright fringe (n = 0) is the brightest, and the other fringes become progressively dimmer. Since the intensity decreases as the order of the fringe increases, we can assume that beyond a certain fringe order, the intensity will be too low to be observed. This fringe order is usually referred to as the maximum order or the maximum number of fringes.

For most cases, this maximum order can be approximated as follows:

n_max = m * L / λ

Where m is a constant usually chosen to be 1 or 2.

Taking m = 1, we have:

n_max = L / λ

From this equation, we can solve for L:

L = λ * n_max

Since we are interested in the maximum number of fringes on either side of the central bright fringe, we double the value of n_max:

n_double_max = 2 * n_max = 2 * λ * n_max

Substituting the values:

n_double_max = 2 * 656 × 10^(-9) m * n_max

Now, we can calculate n_double_max by plugging in the given values. Note that the value of n_max can vary depending on the experimental setup, but we will calculate an approximate value.

Let's assume n_max to be 10. Plugging in the values:

n_double_max = 2 * 656 × 10^(-9) m * 10 = 1.312 × 10^(-5) m

Therefore, at most, about 1.312 × 10^(-5) bright fringes can be formed on either side of the central bright fringe when light of wavelength 656 nm falls on a double slit with a slit separation of 3.45 × 10^(-6) m.