if wavelenght of light use in michelsons inferometre is 400 nm a diametre of 0.05mm and 500 fringes are observed.. then the wavelenght of light used is a.1*10^-7mb.1*10^-8mc. 2*10^-7md. 1.5*10^-7mcorrect ans is option B

To solve the problem regarding the Michelson interferometer, we need to understand the relationship between the wavelength of light, the diameter of the beam, and the number of fringes observed. The key here is to apply the formula that relates these quantities in the context of interference patterns.

Understanding the Interference Pattern

In a Michelson interferometer, when light is split into two beams and then recombined, it creates an interference pattern of bright and dark fringes. The number of fringes observed is directly related to the wavelength of the light used and the path difference between the two beams.

Key Variables

• Wavelength (λ): The distance between successive peaks of the light wave, given as 400 nm (or 400 x 10^-9 m).
• Diameter of the beam (D): The width of the light beam, which is 0.05 mm (or 0.05 x 10^-3 m).
• Number of fringes (N): The total number of fringes observed, which is 500.

Calculating the Wavelength

The formula that relates these variables in the context of a Michelson interferometer is:

N = (2 * D) / λ

Here, the factor of 2 accounts for the round trip of the light beam. Rearranging this formula to solve for the wavelength gives us:

λ = (2 * D) / N

Plugging in the Values

Now, let's substitute the values into the equation:

• D = 0.05 mm = 0.05 x 10^-3 m
• N = 500

Now, substituting these values into the rearranged formula:

λ = (2 * (0.05 x 10^-3 m)) / 500

λ = (0.1 x 10^-3 m) / 500

λ = 0.1 x 10^-3 m / 500 = 0.1 x 10^-6 m / 5 = 2 x 10^-7 m

Final Result

Thus, the wavelength of light used in the Michelson interferometer is 2 x 10^-7 m, which corresponds to option C in your question. However, you mentioned that the correct answer is option B (1 x 10^-8 m). It seems there might be a misunderstanding or miscalculation regarding the options provided. Based on the calculations, the wavelength we derived is indeed 2 x 10^-7 m.

If you have any further questions or need clarification on any part of this process, feel free to ask!