(B) The optical path difference introduced by the slab is $\Delta x = (\mu - 1)t$.Given $\mu = 1.5$ and $t = d/4$,the path difference is $\Delta x = (

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(B) The optical path difference introduced by the slab is $\Delta x = (\mu - 1)t$.Given $\mu = 1.5$ and $t = d/4$,the path difference is $\Delta x = (1.5 - 1) \times (d/4) = 0.5 \times (d/4) = d/8$.For the central maxima to form at a position $y$ on the screen,the path difference at that point must be zero.The path difference at point $y$ is $\Delta x_{net} = \frac{yd}{D} - \Delta x = 0$.Therefore,$\frac{yd}{D} = \frac{d}{8}$.Solving for $y$,we get $y = D/8 = 0.125\ D$.Since the slab is placed in the path $AS_2$,the light through $S_2$ is delayed,causing the central maxima to shift towards the side of the slab,which is below $O$.

Class 12 Physics Wave Optics Variations in YDSE (Young's Double Slit Experiment)

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In a standard $YDSE$ setup,a small transparent slab of thickness $t$ and refractive index $\mu = 1.5$ is placed along the path $AS_2$ (as shown in the figure). Given that the slab thickness $t = d/4$,where $d$ is the slit separation,and the distance from the source $A$ to the slits is not explicitly needed for the shift calculation,find the position of the central maxima on the screen relative to $O$. Assume the distance between the slits and the screen is $D$.

A
$0.125\ D\ m$ above $O$
B
$0.125\ D\ m$ below $O$
C
$0.25\ D\ m$ below $O$
D
$0.25\ D\ m$ above $O$

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Class 12

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Wave Optics

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Variations in YDSE (Young's Double Slit Experiment)

In a double slit experiment,instead of taking slits of equal widths,one slit is made twice as wide as the other. Then in the interference pattern:

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If a thin mica sheet of thickness $t$ and refractive index $\mu = 5/3$ is placed in the path of one of the interfering beams as shown in the figure,then the displacement of the fringe system is:

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In the figure shown in $YDSE$, a parallel beam of light is incident on the slits from a medium of refractive index $n_1$. The wavelength of light in this medium is $\lambda_1$. $A$ transparent slab of thickness $t$ and refractive index $n_3$ is placed in front of one slit. The medium between the screen and the plane of the slits is $n_2$. The phase difference between the light waves reaching point $O$ (symmetrical, relative to the slits) is:

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To make the central fringe appear at the centre $O$ of the screen,a mica sheet of refractive index $\mu = 1.5$ is introduced in front of one of the slits. Choose the correct statement.

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In a double slit experiment, the distance between the slits is $0.1 \ cm$ and the screen is placed at $50 \ cm$ from the slits plane. When one slit is covered with a transparent sheet having thickness $t$ and refractive index $n = 1.5$, the central fringe shifts by $0.2 \ cm$. The value of $t$ is . . . . . . $cm$.

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In a double slit experiment,instead of taking slits of equal widths,one slit is made twice as wide as the other. Then in the interference pattern:

If a thin mica sheet of thickness $t$ and refractive index $\mu = 5/3$ is placed in the path of one of the interfering beams as shown in the figure,then the displacement of the fringe system is:

To make the central fringe appear at the centre $O$ of the screen,a mica sheet of refractive index $\mu = 1.5$ is introduced in front of one of the slits. Choose the correct statement.

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