Question
In $$YSDE,$$ both slits are covered by transparent slab. Upper slit is covered by slab of $$R.I.$$ 1.5 and thickness $$t$$ and lower is covered by $$R.I.$$ $$\frac{4}{3}$$ and thickness $$2t,$$ then central maxima
In $$YSDE,$$ both slits are covered by transparent slab. Upper slit is covered by slab of $$R.I.$$ 1.5 and thickness $$t$$ and lower is covered by $$R.I.$$ $$\frac{4}{3}$$ and thickness $$2t,$$ then central maxima
A.
shifts in $$+ve$$ $$y$$ -axis direction
B.
shifts in $$-ve$$ $$y$$ -axis direction
C.
remains at same position
D.
may shift in upward or downward depending upon wavelength of light
Answer :
shifts in $$-ve$$ $$y$$ -axis direction
Solution :
$$\eqalign{ & \Delta {x_1} = \left( {{\mu _1} - 1} \right)t = \left( {1.5 - 1} \right)t = 0.5\,t \cr & {\text{and}}\,\,\Delta {x_2} = \left( {{\mu _2} - 1} \right)t \times 2t = \left( {\frac{4}{3} - 1} \right) \times 2t = \,\frac{2}{3}t. \cr & {\text{As}}\,\,\Delta {x_2} > \Delta {x_1},\,{\text{so shift will be along}} - ve{\text{ }}y{\text{ - axis}}{\text{.}} \cr} $$
$$\eqalign{ & \Delta {x_1} = \left( {{\mu _1} - 1} \right)t = \left( {1.5 - 1} \right)t = 0.5\,t \cr & {\text{and}}\,\,\Delta {x_2} = \left( {{\mu _2} - 1} \right)t \times 2t = \left( {\frac{4}{3} - 1} \right) \times 2t = \,\frac{2}{3}t. \cr & {\text{As}}\,\,\Delta {x_2} > \Delta {x_1},\,{\text{so shift will be along}} - ve{\text{ }}y{\text{ - axis}}{\text{.}} \cr} $$