Q11Engineering Physics

Question

Answer 1

When a Michelson interferometer is illuminated strictly by a light source emitting two very closely spaced wavelengths (like the sodium D-lines), the resulting interference pattern systematically exhibits distinct positions of absolute maximum distinctness (concordance) and absolute minimum distinctness (discordance or disappearance). This is fundamentally due to the two distinct sets of fringe systems shifting in and out of step.

Given Optical Parameters

Wavelength 1 ( $λ_{1}$ ): $5896 \overset{˚}{A} = 5896 \times 1 0^{- 8} cm$
Wavelength 2 ( $λ_{2}$ ): $5890 \overset{˚}{A} = 5890 \times 1 0^{- 8} cm$

Mathematical Formula and Calculation

The exact physical distance ( $Δ x$ ) the movable mirror must be translated to shift the interference pattern exactly from one position of total disappearance to the very next position of total disappearance is rigorously given by the formula:

Δ x = \frac{λ _{1} λ _{2}}{2 ( λ _{1} - λ _{2} )}

Substituting the exact given values:

Δ x = \frac{( 5896 \times 1 0 ^{- 8} ) \times ( 5890 \times 1 0 ^{- 8} )}{2 \times ( 5896 \times 1 0 ^{- 8} - 5890 \times 1 0 ^{- 8} )}

Δ x = \frac{5896 \times 5890 \times 1 0 ^{- 16}}{2 \times 6 \times 1 0 ^{- 8}} = \frac{34727440 \times 1 0 ^{- 16}}{12 \times 1 0 ^{- 8}}

Δ x \approx 2893953 \times 1 0^{- 8} cm = 0.0289 cm = 0.289 mm

Q11Engineering Physics

Question

Answer

Given Optical Parameters

Mathematical Formula and Calculation