Question 18: Wave Optics

Question

In a young's double slit arrangement fringes are produced using light of wavelength 4000 $$\mathop A\limits^o $$. One slit is covered by a thin plate of glass of refractive index 1.4 and the other with another glass plate of same thickness but of refractive index 1.7. By doing so the central bright shifts to original sixth fringe from centre. Thickness of glass plate is ................. .

Accepted Answer

As, shift $$\Delta x = {\beta  \over \lambda }(\mu  - 1)t$$
Shift due to one plate $$\Delta {x_1} = {\beta  \over \lambda }({\mu _1} - 1)t$$
Shift due to another path $$\Delta {x_2} = {\beta  \over \lambda }({\mu _2} - 1)t$$
Net shift $$\Delta x = \Delta {x_2} - \Delta {x_1} = {\beta  \over \lambda }({\mu _2} - {\mu _1})t$$ ..... (i)
Also, it is given that $$\Delta$$x = 6$$\beta$$
Hence, $$6\beta  = {\beta  \over \lambda }({\mu _1} - {\mu _2})t$$
$$ \Rightarrow t = {{6\lambda } \over {({\mu _1} - {\mu _2})}} = {{6 	imes 4000} \over {(1.7 - 1.4)}} - 80000\,\mathop A\limits^o $$
$$ \Rightarrow t = 8 	imes {10^{ - 6}} = 8\mu $$m

Answer

2 $$\mu$$m

Answer

8 $$\mu$$m

Answer

11 $$\mu$$m

Answer

16 $$\mu$$m

Wave Optics

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