Question

in a michelsons interferometer 200 fringes cross the field of view when the movable mirror is displaced throgh 0.0589 mm​

Answer 1

Answer:

When the movable mirror of a Michaelson Interferometer is shifted through 0.0589 mm, 200 fringes cross the field. What is the wavelength of the light? = 6000 Å.

Answer 2

Given:

• The number of fringes cross the field is $200$.
• The mirror displaced through $0.0589mm$.

To find:

• The wavelength of the light.

Step-by-step explanation:

• The Michelson's interferometer is used to measure the wavelength of the optical beam by the creation of interference patterns.
• The Michelson's interferometer device is very important in the history since in provides a simple interferometric configuration which is used to introduce basic principles.
• Let the number of fringes cross be $N$.
• We know that the number of fringes cross the field of view is $200$, so,

       $N=200$

• Let the mirror is moved through the known distance $d$.
• We know that the mirror is displaced through $0.0589mm$, so,

        $d=0.0589mm$

• Convert Millimetres into metres.
• By converting we get the distance as,

        $d=0.0589$×$10^{-3} m$

• To find the wavelength of the light we have a formula,

        λ$=\frac{2d}{N}$

• By substituting the values in the formula we get,

        λ$=\frac{2(0.0589)(10^-3)}{200}$

• By solving the above equation we get the wavelength of the light as,

        λ$=5890$Α

Final answer:

• Therefore the wavelength of the light is λ$=5890$Α.