Question

Koster's modification of Michelson interferometer is used to determine the thickness of a gauge $G$. The gauge $G$ is placed on the mirror $M_2$ as shown in figure (a). The field-of-view observed through the lens L is shown in figure (b). The fractional-fringe shift e, as shown in figure (b), is measured to be 0.15 when the wavelength of light used is $0.63\mu \text{m}$. A quick check with a micrometer shows that the gauge length is approximately $100\mu \text{m}$. Then an accurate estimate of gauge length, in $\mu \text{m}$, is

• A. 99.902
• B. 101.706
• C. 100.804
• D. 100.000

Answer 1

The correct option is A 99.902

Given fractional fringe shift, $e=0.15$
and $\lambda$ of light used $=0.63\mu \text{m}$
$\Rightarrow$ Error in length of gauge $=e.\lambda =0.0945\mu \text{m}$
So, Actual length $=100-0.0945\simeq 99.9055$
$\simeq 99.902\mu \text{m}$