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Effect of Introducing a Thin Transparent Plate in the Path of One Way

Let 51 and 52 be two monochromatic coherent sources of wavelength A. Let a thin plate of thickness t and refractive index , µ is introduced in the path of one ray from source S1 as shown in Figure 4.2. Now, this ray travel partially in the material if c and v are the velocities of light in air and medium respectively then path difference between two rays.


(S2P-S1P) = [(S2P)air– {(S1P- t)air + (t)plate}] . .. (1)

= [(S2P- SlP )air + (tair– tplate)]




we know that distance t travelled by light through plate is equivalent to a distance µt travelled in air.


Path difference = [(S2P- SlP) + t – µt]air


= [S2P- SlP – (µ – 1) t]


= [yd/D -(µ-1)t]

For maxima


Path difference = [ yd/D – (µ-1)t]= nλ

y   = d [  nλ + (µ – 1) t]



Without plate (i.e. t = 0) the’ position of maximum is given by


y0 = nDλ/d


The plate causes a shift of maximum and minimum by an account.


δ’ = (y- y0) = D/d (µ- 1) t

We know that

β = λD/d   =>  D/d = β/λ


δ’ = β/λ(µ- 1) t


where β is fringe width


This shift is +ve if µ > 1 and the pattern will move by an amount δ’ toward the side on

which the plate is placed keeping the nature of pattern same.


If the central fringe moves through a distance formely occupied by the nth bright fringe


δ’ = nβ =β/λ(µ- 1) t

n=(µ- 1) t/λ

The gives the number of bands through which the system has shifted.