Interference Pattern and Order

In an interference pattern, the phenomenon of interference occurs when two or more waves meet at a point. This leads to the formation of alternate bright and dark fringes. The order of a bright fringe is determined by the number of wavelengths that fit into the path difference between the interfering waves.

16th Order Maximum for λ = 6000 Å

The given problem states that at a certain point in the interference pattern, the 16th order maximum is observed for a wavelength (λ) of 6000 Å (angstroms). This means that the path difference between the interfering waves at that particular point is such that the 16th bright fringe is formed.

Calculating the Path Difference

To find the order of the bright fringe when the source is replaced by light of a different wavelength (λ2 = 4800 Å), we need to calculate the new path difference. The formula to calculate the path difference for interference is given by:

Path Difference = m * λ

where m is the order of the bright fringe and λ is the wavelength of the light.

Using this formula, we can calculate the original path difference for the 16th order maximum with λ1 = 6000 Å:

Path Difference1 = 16 * 6000 Å

Calculating the New Order

Now, let's calculate the new order of the bright fringe when the wavelength is λ2 = 4800 Å. We can rearrange the formula to solve for the order:

m = Path Difference2 / λ2

where Path Difference2 is the new path difference and λ2 is the new wavelength.

Substituting the values, we get:

m = Path Difference1 / λ2

m = (16 * 6000 Å) / 4800 Å

Simplifying the expression:

m = 20

Therefore, the order of the bright fringe for λ2 = 4800 Å is 20.

Explanation

When the source is replaced by light of a different wavelength, the order of the bright fringes changes. This is because the path difference between the interfering waves is directly proportional to the wavelength. As the wavelength changes, the number of wavelengths that fit into the path difference also changes, leading to a different order for the bright fringe.

In this case, the order increases from 16 to 20 when the wavelength changes from 6000 Å to 4800 Å. This means that the bright fringe becomes wider and shifts further away from the central maximum.

This phenomenon can be explained by the interference of light waves. When the waves interfere constructively, a bright fringe is formed, and when they interfere destructively, a dark fringe is formed. The order of the bright fringe depends on the path difference between the waves, which in turn depends on the wavelength of the light.