Question

In Michelson’s interferometer 500 fringes cross the field of view when the movable mirror is displaced through 0.147 mm. calculate the wavelength of monochromatic light used.In Michelson’s interferometer 100 fringes cross the field of view when the movable mirror is displaced through 0.02948 mm. calculate the wavelength of monochromatic light used.​

Answer 1

Answer:

field of view when the movable mirror is displaced through 0.147 mm. calculate the wavelength of monochromatic light used.In Michelson’s interferometer 100 fringes cross the field of view when the movable mirror is displaced through 0.02948 mm. calculate the wavelength of monochromatic

Answer 2

Answer:

Explanation:

Concept:

Monochromatic light definition:

Single-wavelength light sources are known as monochromatic lights, where mono stands for only one and chroma for colour. Monochromatic lights are defined as visible light that falls inside a specific range of wavelengths. It has a wavelength that falls within a constrained wavelength range.

Fringes definition:

Fringes are contrasted regions of light or darkness created by the diffraction or interference of radiation with a measured wavelength in physics.

Given:

Mirror move by distance (d$1$)$=0.147mm$

Number of fringes that appear at the center (N$1$) $=500$

Mirror move by distance (d$2$) $= 0.02948 mm$

Number of fringes that appear at the center (N$2$) $= 100$

Find:

We have to find the wavelength(λ1, λ2)of the monochromatic light used.

Solution:

Given that Mirror move by distance (d$1$)$=0.147mm$

                 Number of fringes that appear at the center (N$1$) $=500$

                 Mirror move by distance (d$2$) $= 0.02948 mm$

                 Number of fringes that appear at the center (N$2$) $= 100$

We are aware that the formula for wavelength in the Michelson's interferometer:

λ  $=2d / N$

λ$1$ $=2d1/N1$

   $=2\times0.147mm/500$

   $=0.294/500$

λ$1$  $=0.588\times10^{-3} mm$

λ$2=2d2/N2$

    $= 2\times0.02948 mm / 100$

   $= 0.05896 / 100$

λ$2 = 0.5896 \times 10^-3 mm$

Hence the wavelength λ$1=0.588\times10^{-3} mm$,λ$2=0.5896\times10^{-3}mm$ of the monochromatic light used.

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