Question

Light of wavelength \(6000 \, \text{Å}\) is incident on a thin glass plate of refractive index \(1.5\) such that the angle of refraction into the plate is \(60^\circ\). Calculate the smallest thickness of the plate which will make a dark fringe by reflected beam interference.

• A. \(1.5 \times 10^{-7} \, \text{m}\)
• B. \(2 \times 10^{-7} \, \text{m}\)
• C. \(3.5 \times 10^{-7} \, \text{m}\)
• D. \(4 \times 10^{-7} \, \text{m}\)

Hint:

Use the thin-film interference formula to calculate the thickness of the film for dark fringes, keeping in mind the refractive index and the angle of refraction.