In Young's double slit experiment a mica plate of refractive index μ is introduced in the path of light coming from one of the slit. If the central bright fringe gets shifted to the point originally occupied by the fourth bright fringe, then the thickness of the mica plate will be (symbols have their usual meaning)

Question

In Young's double slit experiment a mica plate of refractive index μ is introduced in the path of light coming from one of the slit. If the central bright fringe gets shifted to the point originally occupied by the fourth bright fringe, then the thickness of the mica plate will be (symbols have their usual meaning) (A) (2 λ /(. μ - 1 .)) (B) (4 λ /3 (. μ - 1 .)) (C) (4 λ /(. μ - 1 .)) (D) (2 λ /3 (. μ - 1 .))

Tardigrade Admin · Accepted Answer

Position of fourth bright =((4 λ D/d)) According to given condition ((. μ - 1 .) t D/d)=(4 λ D/d) t=(4 λ /μ - 1)

$\frac{2 λ}{( μ - 1 )}$

$\frac{4 λ}{3 ( μ - 1 )}$

$\frac{4 λ}{( μ - 1 )}$

$\frac{2 λ}{3 ( μ - 1 )}$

Position of fourth bright $= (\frac{4 λ D}{d})$
According to given condition $\frac{( μ - 1 ) t D}{d} = \frac{4 λ D}{d}$
$t = \frac{4 λ}{μ - 1}$

(μ−1)2λ​

3(μ−1)4λ​

(μ−1)4λ​

3(μ−1)2λ​

Position of fourth bright =(d4λD​) According to given condition d(μ−1)tD​=d4λD​ t=μ−14λ​

$\frac{2 λ}{( μ - 1 )}$

$\frac{4 λ}{3 ( μ - 1 )}$

$\frac{4 λ}{( μ - 1 )}$

$\frac{2 λ}{3 ( μ - 1 )}$

Position of fourth bright $= (\frac{4 λ D}{d})$
According to given condition $\frac{( μ - 1 ) t D}{d} = \frac{4 λ D}{d}$
$t = \frac{4 λ}{μ - 1}$