(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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Two parallel rays of red and violet colour pass through a glass slab. Which of the following is correct?

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$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

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$A$ narrow,paraxial beam of light is converging towards a point $I$ on a screen. $A$ plane parallel plate of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by

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Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

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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 $,cm$)?

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Two parallel rays of red and violet colour pass through a glass slab. Which of the following is correct?

$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

$A$ narrow,paraxial beam of light is converging towards a point $I$ on a screen. $A$ plane parallel plate of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by

Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

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