Question

In YDSE, source is red light of wavelength $7\times {10}^{-7}m$. When a thin glass plate of refractive index 1.5 is put in the path of one of the interfering beams, the central bright fringe shifts by ${10}^{-3}$ m to the position previously occupied by the $5^{th}$ bright fringe. Find the thickness of the plate. When the source is now changed to green light of wavelength $5\times {10}^{-7}m$, the central fringe shifts to a position initially occupied by the $6^{th}$ bright fringe due to red light. Find the refractive index of glass for the green light.

• A. 1.6
  
• B. 1.8
  
• C. 2
• D. None of these

Answer 1

The correct option is A 1.6


(a) $t({\mu }_1-1)\frac{D}{d}=5{\beta }_R=5\frac{{\lambda }_{R}D}{d}\Rightarrow t=7\times {10}^{-6}m$ after substitution.
(b) $t({\mu }_2-1)\frac{D}{d}=6\frac{{\lambda }_{R}D}{d}\Rightarrow \mu =1.6$ after substitution.