(D) The apparent depth of an object in a medium of refractive index $\mu$ and real depth $h$ is given by $h_{app} = \frac{h}{\mu}$.For multiple layers

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(D) The apparent depth of an object in a medium of refractive index $\mu$ and real depth $h$ is given by $h_{app} = \frac{h}{\mu}$.For multiple layers of immiscible liquids,the total apparent depth is the sum of the apparent depths of each layer:$h_{app} = \frac{h_1}{\mu_1} + \frac{h_2}{\mu_2}$Given:$h_1 = 6 \,cm, \mu_1 = \frac{8}{5}$$h_2 = 6 \,cm, \mu_2 = \frac{3}{2}$Substituting the values:$h_{app} = \frac{6}{8/5} + \frac{6}{3/2}$$h_{app} = \frac{30}{8} + \frac{12}{3}$$h_{app} = \frac{15}{4} + 4 = \frac{15 + 16}{4} = \frac{31}{4} \,cm$Comparing this with the given apparent depth $\frac{\alpha}{4} \,cm$,we get $\alpha = 31$.

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

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Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6 \,cm$. $A$ coin is placed at the bottom of the beaker. For near normal vision,the apparent depth of the coin is $\frac{\alpha}{4} \,cm$. The value of $\alpha$ is . . . . . . .

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A
$64$
B
$85$
C
$65$
D
$31$

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Ray Optics and Optical Instruments

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Refraction through Plane Surface and Glass Slab

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Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. $A$ dot is made at the bottom of the beaker. For near normal vision,find the apparent depth of the dot.

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An empty tank has a concave mirror at its bottom. When sunlight falls normally on the mirror, it is focused at a height of $32 \,cm$ from the mirror. If the tank is filled with water up to a height of $20 \,cm$, then the sunlight focuses at (refractive index of water $= 4/3$):

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When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is:

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Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.

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$A$ glass cube of length $21 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,its apparent distance is $8 \ cm$. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are:

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Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. $A$ dot is made at the bottom of the beaker. For near normal vision,find the apparent depth of the dot.

An empty tank has a concave mirror at its bottom. When sunlight falls normally on the mirror, it is focused at a height of $32 \,cm$ from the mirror. If the tank is filled with water up to a height of $20 \,cm$, then the sunlight focuses at (refractive index of water $= 4/3$):

When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is:

Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.

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