(A) Let the distance of the air bubble from the first surface be $l_1$ and from the second surface be $l_2$. The total length of the cube is $L = 24 \

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(A) Let the distance of the air bubble from the first surface be $l_1$ and from the second surface be $l_2$. The total length of the cube is $L = 24 \,cm$. Thus, $l_1 + l_2 = 24 \,cm$, which implies $l_2 = 24 - l_1$.The formula for apparent depth is given by $\mu = \frac{\text{Real depth}}{\text{Apparent depth}}$.For the first surface:$\mu = \frac{l_1}{10} \quad \dots(i)$For the second surface:$\mu = \frac{l_2}{6} = \frac{24 - l_1}{6} \quad \dots(ii)$Equating $(i)$ and $(ii)$:$\frac{l_1}{10} = \frac{24 - l_1}{6}$$6l_1 = 10(24 - l_1)$$6l_1 = 240 - 10l_1$$16l_1 = 240$$l_1 = \frac{240}{16} = 15 \,cm$Therefore, the distance of the air bubble from the first surface is $15 \,cm$.

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

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$A$ transparent glass cube of length $24 \,cm$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $10 \,cm$ from the surface. When seen normally from the opposite surface, its apparent distance is $6 \,cm$. The distance of the air bubble from the first surface is (in $\,cm$)

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A
$15$
B
$14$
C
$12$
D
$8$

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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

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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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$A$ 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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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.

Each quarter of a vessel of depth $H$ is filled with liquids of the refractive indices $n_1, n_2, n_3$ and $n_4$ from the bottom respectively. The apparent depth of the vessel when looked normally is

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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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