Question

An experiment with a Michelson interferometer is performed in vacuum using a laser of wavelength 610 nm. One beam passes through a glass cavity 1.3 cm long. When the cavity is filled with a medium of refractive index \( n \), 472 dark fringes move past a reference line. The speed of light is \( 3\times10^8 \) m/s. The value of \( n \) is:

• A. 1.01
• B. 1.04
• C. 1.06
• D. 1.10

Hint:

In Michelson interferometer, the number of shifted fringes is directly proportional to the optical path difference introduced by the medium.

Answer 1

The Correct Option is A

Step 1: Relation between fringe shift and refractive index.
Number of fringes shifted \( N = \frac{2 t (n - 1)}{\lambda}. \) Step 2: Substitute the known values.
\[ 472 = \frac{2(1.3 \times 10^{-2})(n - 1)}{610 \times 10^{-9}}. \] \[ n - 1 = \frac{472 \times 610 \times 10^{-9}}{2.6 \times 10^{-2}} = 0.060. \] \[ n = 1.06. \]
Step 3: Final Answer.
Refractive index \( n = 1.06. \)