(D) The shift in the central maximum due to the introduction of a glass plate of thickness $t$ and refractive index $\mu$ is given by the formula: $\D

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(D) The shift in the central maximum due to the introduction of a glass plate of thickness $t$ and refractive index $\mu$ is given by the formula: $\Delta x = \frac{(\mu - 1) t D}{d}$.Given that the central maximum shifts to the position of the $4^{th}$ bright fringe, the shift is equal to the path difference of the $4^{th}$ bright fringe, which is $4\lambda$.Equating the path difference introduced by the glass plate to the shift: $(\mu - 1) t = n \lambda$.Substituting the given values: $(1.5 - 1) t = 4 \times 500 \, nm$.$0.5 \times t = 2000 \, nm$.$t = 4000 \, nm$.Since $1 \, \mu m = 1000 \, nm$, we have $t = 4 \, \mu m$.

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

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Monochromatic light of wavelength $500 \, nm$ is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index $= 1.5$), the central maximum is shifted to a position previously occupied by the $4^{th}$ bright fringe. The thickness of the glass plate is ..................... $\mu m$.

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Variations in YDSE (Young's Double Slit Experiment)

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In the given figure,light is incident at an angle $\theta$ with the normal to a plane containing two slits of separation $d$. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $\theta$ and outgoing angle $\phi$.

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$A$ thin mica sheet of thickness $2 \times 10^{-6} \ m$ and refractive index $\mu = 1.5$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 \ \mathring{A}$. The central bright maximum will shift:

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$A$ parallel beam of light of wavelength $500 \ nm$ is incident at an angle $30^o$ with the normal to the slit plane in a Young's double-slit experiment. The intensity due to each slit is $I_o$. Point $O$ is equidistant from $S_1$ and $S_2$. The distance between the slits is $1 \ mm$.

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In the setup shown in the figure,the two slits,$S_1$ and $S_2$,are not equidistant from the slit $S$. The central fringe at $O$ is then

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$A$ thin plastic sheet of refractive index $1.6$ is used to cover one of the slits of a double slit arrangement. The central point on the screen is now occupied by what would have been the $7^{th}$ bright fringe before the plastic was used. If the wavelength of light is $600 \ nm$, what is the thickness (in $\mu m$) of the plastic sheet?

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In the given figure,light is incident at an angle $\theta$ with the normal to a plane containing two slits of separation $d$. Select the expression that correctly describes the positions of the interference maxima in terms of the incoming angle $\theta$ and outgoing angle $\phi$.

$A$ thin mica sheet of thickness $2 \times 10^{-6} \ m$ and refractive index $\mu = 1.5$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 \ \mathring{A}$. The central bright maximum will shift:

$A$ parallel beam of light of wavelength $500 \ nm$ is incident at an angle $30^o$ with the normal to the slit plane in a Young's double-slit experiment. The intensity due to each slit is $I_o$. Point $O$ is equidistant from $S_1$ and $S_2$. The distance between the slits is $1 \ mm$.

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