Question 356: Waves Optics

Question

The path difference between two interfering light waves meeting at a point on the screen is $$\left(\frac{57}{2}\right) \lambda$$. The bond obtained at that point is

Accepted Answer

The interference pattern formed by light waves is characterized by alternating bright and dark bands (fringes). The path difference between two interfering waves determines whether we get a bright or dark band at a specific point. The criterion for these bands based on the path difference can be stated as follows:
For the bright band (constructive interference):
$$\Delta x = m\lambda$$
where $ \Delta x $ is the path difference, $ m $ is any integer (0, 1, 2, 3, ...), and $ \lambda $ is the wavelength of light.
For the dark band (destructive interference):
$$\Delta x = (m + \frac{1}{2}) \lambda$$
where $ m $ is any integer (0, 1, 2, 3, ...).
Given that the path difference is:
$$\Delta x = \frac{57}{2} \lambda$$
We observe that:
$$\frac{57}{2} = 28.5$$
This suggests that the path difference is equal to $ (28.5) \lambda $. Hence, this can be expressed in terms of the dark band condition:
$$\Delta x = (28 + \frac{1}{2}) \lambda$$
This matches the formula for the dark band, with $ m = 28 $. Therefore, the point corresponds to the 29
th
dark band (since we start counting from m = 0).
Hence, the correct answer is:
Option D: 29
th
dark band

Answer

29th bright band

Answer

57th dark band

Answer

57th bright band

Answer

29th dark band

Waves Optics

The path difference between two interfering light waves meeting at a point on the screen is $\left(\frac{57}{2}\right) \lambda$. The bond obtained at that point is

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