the otical path difference between two identical waves arriving at a point in 0.05cm.if wavelength of light used is 5000angstron unit den the no of dark fringes passing throught that point will be??

To determine the number of dark fringes that pass through a point where two identical waves meet, we first need to understand the concept of optical path difference (OPD) and how it relates to interference patterns. In this case, we have an optical path difference of 0.05 cm and a wavelength of light at 5000 angstroms. Let's break this down step by step.

Understanding Optical Path Difference

The optical path difference is the difference in the distance traveled by two waves arriving at the same point. When this difference is a multiple of the wavelength, constructive interference occurs, leading to bright fringes. Conversely, when the OPD is an odd multiple of half the wavelength, destructive interference occurs, resulting in dark fringes.

Converting Units

First, we need to convert the given values into consistent units. The optical path difference is given as:

• 0.05 cm = 0.05 × 10^-2 m = 5 × 10^-3 m

The wavelength of light is given as:

• 5000 angstroms = 5000 × 10^-10 m = 5 × 10^-7 m

Calculating the Number of Dark Fringes

To find the number of dark fringes, we can use the formula for the condition of destructive interference:

• OPD = (m + 0.5) × λ

Here, m is an integer (0, 1, 2, ...). We can rearrange this to find m:

• m = (OPD / λ) - 0.5

Substituting the values we have:

• m = (5 × 10^-3 m) / (5 × 10^-7 m) - 0.5
• m = 10,000 - 0.5
• m ≈ 9,999.5

Interpreting the Result

Since m must be an integer, we can take the integer part of 9,999.5, which is 9,999. This means there are 9,999 dark fringes that can be observed at that point. Each dark fringe corresponds to a specific condition of destructive interference where the waves cancel each other out.

Final Thoughts

In summary, with an optical path difference of 0.05 cm and a wavelength of 5000 angstroms, we find that approximately 9,999 dark fringes will pass through the point of interest. This illustrates the fascinating interplay of light waves and how they can create intricate patterns based on their phase relationships.