(C) Let $h$ be the height of the ball above the water surface. The velocity of the ball at height $h$ is given by $v_b = \sqrt{2g(H - h)}$, where $H =

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(C) Let $h$ be the height of the ball above the water surface. The velocity of the ball at height $h$ is given by $v_b = \sqrt{2g(H - h)}$, where $H = 20 \,m$ is the initial height and $h = 12.8 \,m$.$v_b = \sqrt{2 \times 10 \times (20 - 12.8)} = \sqrt{20 \times 7.2} = \sqrt{144} = 12 \,m/s$.When an object is in a rarer medium (air) and viewed from a denser medium (water), the apparent height $h'$ is given by $h' = \mu h$, where $\mu = 4/3$ is the refractive index of water.Therefore, the apparent velocity $v_a$ as seen by the fish is $v_a = \frac{d}{dt}(h') = \mu \frac{dh}{dt} = \mu v_b$.$v_a = (4/3) \times 12 \,m/s = 16 \,m/s$.

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

Difficult

$A$ ball is dropped from a height of $20 \,m$ above the surface of water in a lake. The refractive index of water is $4/3$. $A$ fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \,m$ above the water surface, the fish sees the speed of the ball as (Take $g = 10 \,m/s^2$): (in $\,m/s$)

IIT 2009 All IIT

A
$9$
B
$12$
C
$16$
D
$21.33$

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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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$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

MediumAIPMT 2000

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Assume the situation shown in the figure. Water $(\mu_w = 4/3)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ above the water surface. The distance of the image of the object $O$ from the mirror is ...... $cm$.

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To a bird in air, a fish in water appears to be at $30 \,cm$ from the surface. If the refractive index of water with respect to air is $\frac{4}{3}$, the real depth of the fish from the surface is: (in $\,cm$)

DifficultMHT CET 2022

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An underwater swimmer is at a depth of $12 \, m$ below the surface of water. $A$ bird is at a height of $18 \, m$ from the surface of water,directly above his eyes. For the swimmer,the bird appears to be at a distance from the surface of water equal to ....... $m$ (Refractive index of water is $4/3$).

Easy

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$A$ slab of glass,of thickness $6\, cm$ and refractive index $1.5$,is placed in front of a concave mirror,the faces of the slab being perpendicular to the principal axis of the mirror. If the radius of curvature of the mirror is $40\, cm$ and the reflected image coincides with the object,then the distance of the object from the mirror is.....$cm$

Medium

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$A$ bubble in a glass slab $(\mu = 1.5)$ when viewed from one side appears at $5 \ cm$ and from the other side appears at $2 \ cm$. The thickness of the slab is .... $cm$.

Assume the situation shown in the figure. Water $(\mu_w = 4/3)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ above the water surface. The distance of the image of the object $O$ from the mirror is ...... $cm$.

To a bird in air, a fish in water appears to be at $30 \,cm$ from the surface. If the refractive index of water with respect to air is $\frac{4}{3}$, the real depth of the fish from the surface is: (in $\,cm$)

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