(A) The apparent depth $d'$ is given by the formula $d' = \frac{d}{\mu}$,where $d$ is the real depth and $\mu$ is the refractive index of the liquid.F

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(A) The apparent depth $d'$ is given by the formula $d' = \frac{d}{\mu}$,where $d$ is the real depth and $\mu$ is the refractive index of the liquid.For water,the apparent depth is $9.4\,cm$ with $\mu_1 = 1.33$ and $d = 12.5\,cm$.When water is replaced by a liquid with $\mu_2 = 1.5$,the new apparent depth $d_2$ is:$d_2 = \frac{12.5}{1.5} \approx 8.33\,cm$.The microscope was initially focused at $9.4\,cm$. To focus on the needle again,it must be moved by the difference in apparent depths:$\Delta d = 9.4 - 8.33 = 1.07\,cm \approx 1.1\,cm$.

Class 12 Physics Ray Optics and Optical Instruments Refraction through Plane Surface and Glass Slab

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The apparent depth of a needle lying at the bottom of a tank,which is filled with water of refractive index $1.33$ to a height of $12.5\,cm$,is measured by a microscope to be $9.4\,cm$. If water is replaced by a liquid of refractive index $1.5$ up to the same height,what distance would the microscope have to be moved to focus on the needle again (in $,cm$)?

A
$1.1$
B
$2.13$
C
$3.1$
D
$4.15$

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Class 12

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Ray Optics and Optical Instruments

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Refraction through Plane Surface and Glass Slab

$A$ flat glass slab of thickness $6\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An observer is standing behind the glass slab and looking at the mirror. The actual distance of the observer from the mirror is $50\, cm$. The distance of his image from himself,as seen by the observer is .......$cm$.

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$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is

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$A$ glass slab of thickness $3 \, cm$ and refractive index $3/2$ is placed on an ink mark on a piece of paper. The mark is viewed from a distance of $5.0 \, cm$ above the top surface of the slab. At what distance (in $cm$) will the mark appear to be?

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An air bubble in a glass slab $(\mu = 1.5)$ appears to be $5 \, cm$ deep when viewed through one face and $2 \, cm$ deep when viewed through the opposite face. What is the thickness of the slab in $cm$?

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Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are $3 \ cm, 4 \ cm$ and $6 \ cm$ respectively. The apparent depth of the vessel is (in $cm$)

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