(B) When a glass plate of refractive index $\mu$ and thickness $t$ is introduced in the path of one of the beams,the additional path difference introd

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(B) When a glass plate of refractive index $\mu$ and thickness $t$ is introduced in the path of one of the beams,the additional path difference introduced is $\Delta p = (\mu - 1)t$.For the intensity at the original central position $O$ to remain unchanged (i.e.,to remain a maximum),the path difference must be an integral multiple of the wavelength $\lambda$.Therefore,$\Delta p = n \lambda$,where $n = 1, 2, 3, \dots$Given $\mu = 1.5$ and $t = x \lambda$,we have:$(\mu - 1)t = n \lambda$$(1.5 - 1) (x \lambda) = n \lambda$$0.5 x \lambda = n \lambda$$0.5 x = n$$x = 2n$For the smallest non-zero value of $x$,we take $n = 1$,which gives $x = 2(1) = 2$.

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

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In Young's double-slit experiment performed using a monochromatic light of wavelength $\lambda$,when a glass plate $(\mu=1.5)$ of thickness $t = x \lambda$ is introduced in the path of one of the interfering beams,the intensity at the position where the central maximum occurred previously remains unchanged. The value of $x$ will be..........

JEE MAIN 2022 All JEE MAIN

A
$3$
B
$2$
C
$1.5$
D
$0.5$

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Wave Optics

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Variations in YDSE (Young's Double Slit Experiment)

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When one of the slits in Young's experiment is covered with a transparent sheet of thickness $3.6 \times 10^{-3} \ cm$,the central fringe shifts to a position originally occupied by the $30^{th}$ bright fringe. If $\lambda = 6000 \ \mathring{A}$,then what is the refractive index of the sheet?

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In the figure shown,if a parallel beam of white light is incident on the plane of the slits,then the distance of the white spot on the screen from $O$ is [Assume $d << D, \lambda << d$].

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As shown in the figure,two coherent sources $S_1$ and $S_2$ are separated by a very small distance $d$. The fringes produced on the screen will be ........

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Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between them is $2 \lambda$ as shown in the figure. The first bright fringe is formed at $P$ due to interference on a screen placed at a distance $D$ from $S_1$ $(D >> \lambda)$. Find the distance $OP$.

DifficultTS EAMCET 2012

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The figure shows a double-slit experiment. Each slit has a width $W$. $A$ thin glass slab of thickness $\delta$ and refractive index $\mu$ is placed in front of one of the slits. The intensity at the central point $C$ is measured as a function of the thickness $\delta$. At what thickness $\delta$ will the intensity at $C$ be minimum?

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When one of the slits in Young's experiment is covered with a transparent sheet of thickness $3.6 \times 10^{-3} \ cm$,the central fringe shifts to a position originally occupied by the $30^{th}$ bright fringe. If $\lambda = 6000 \ \mathring{A}$,then what is the refractive index of the sheet?

In the figure shown,if a parallel beam of white light is incident on the plane of the slits,then the distance of the white spot on the screen from $O$ is [Assume $d << D, \lambda << d$].

As shown in the figure,two coherent sources $S_1$ and $S_2$ are separated by a very small distance $d$. The fringes produced on the screen will be ........

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