The central fringe of the interference pattern produced by the light of wavelength 6000 $\AA$ is fou

Question

The central fringe of the interference pattern produced by the light of wavelength 6000 $\AA$ is found to shift to the position of $4^{	ext {th }}$ bright fringe after a glass sheet of refractive index 1.5 is introduced. The thickness of glass sheet would be

Professor PC Thomas Classes · Answer

The shift is given by $(\mu - 1)t = n\lambda$. For $n=4, \lambda = 6000	ext{\AA}, \mu=1.5$, we have $(1.5-1)t = 4 	imes 6000 	imes 10^{-10} \implies 0.5t = 24000 	imes 10^{-10} \implies t = 4.8 	imes 10^{-6} 	ext{ m} = 4.8 \mu	ext{m}$. Correct Option is A.