In the ideal double-slit experiment, when a glass-plate (refractive index 1 . 5 ) of thickness t is introduced in the path of one of the interfering beams (wavelength λ ), the intensity at the positio

Question

In the ideal double-slit experiment, when a glass-plate (refractive index 1 . 5 ) of thickness t is introduced in the path of one of the interfering beams (wavelength λ ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

TestHub · Accepted Answer

For no change of Intensity at central maxima there should again be maxima.

$∴$ Path difference due to slab should be integral multiple of $λ$

or $Δ x = n λ$

or $(μ - 1) t = λ n = 1, 2, 3,........$

or $t = \frac{n λ}{μ - 1}$

For minimum value of $t, n = 1$

$t = \frac{λ}{μ - 1} = \frac{λ}{1 \cdot 5 - 1} = 2 λ$

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