Class 11 > Unit # 13: Physical Optics > Michelson Interferometer

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Michelson’s Interferometer: Construction, Working & Wavelength Calculation

Video Lecture: Michelson’s Interferometer

Watch the complete step-by-step video lecture explaining the construction, optical pathway, and wavelength calculation using Michelson’s Interferometer:

Introduction

“Michelson’s interferometer was invented by the American physicist A.A. Michelson. Unlike Young’s double-slit experiment which uses two narrow slits, a Michelson’s interferometer utilizes an extended source of monochromatic light.”

It is a precision optical instrument based on the division of amplitude, capable of producing interference fringes by splitting a beam of light into two paths, reflecting them from mirrors, and recombining them.

Fig: Principle diagram of Michelson’s interferometer showing beam splitting and mirror paths.

Construction and Working Procedure

Light from an extended monochromatic source strikes glass plate $C$ (known as the beam splitter), the rear surface of which has a thin semi-transparent silver coating:

• Beam 1 (Reflected Path): Part of the light is reflected from the silvered surface towards mirror $M_1$. After reflection from $M_1$, it travels back through plate $C$ to reach the observer’s eye.
• Beam 2 (Transmitted Path): The remainder of the light passes through the silvered surface of $C$, travels through the compensator plate $D$, and reflects off mirror $M_2$. It then returns through plate $D$ and reflects off the silvered surface of $C$ to the observer’s eye.

Role of Compensator Plate $D$: Both plates $C$ and $D$ are made of the exact same thickness of glass. Plate $D$ ensures that Beam 2 passes through the same thickness of glass as Beam 1 (which traverses plate $C$ three times), compensating for any optical path differences introduced by the glass material itself.

If the distances $L_1$ and $L_2$ from the beam splitter to mirrors $M_1$ and $M_2$ are nearly equal, and the mirrors are adjusted, circular or wedge-shaped interference fringes are observed through the telescope.

Calculation of Wavelength

Michelson’s interferometer can be used to measure the wavelength $\lambda$ of monochromatic light with high precision. Let $\lambda$ be the wavelength of light from the extended source:

• If movable mirror $M_2$ is translated through a distance of $\frac{\lambda}{4}$, the round-trip path difference changes by $2 \times \left(\frac{\lambda}{4}\right) = \frac{\lambda}{2}$, causing a dark fringe to replace a bright fringe.
• If mirror $M_2$ is moved through a distance of $\frac{\lambda}{2}$, the path difference changes by $\lambda$, shifting the fringe pattern by one full fringe order.

If $m$ bright fringes pass across the cross-wire of the telescope when mirror $M_2$ is moved through a total measured distance $X$, the relationship is given by:

$X = m \left(\frac{\lambda}{2}\right)$

Rearranging the equation to solve for the wavelength $\lambda$:

$\lambda = \frac{2X}{m}$

Because $m$ can be chosen to be very large over a macroscopic displacement $X$, the distance $X$ can be measured with exceptional precision, yielding a highly accurate value for the wavelength $\lambda$.

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