Q: A coin is placed at the bottom of a beaker containing water (refractive index \$= 4/3\$) to a depth of \$12 cm\$. By what height the coin appears to be raised when seen from vertically above?

\$ RI=\dfrac{\text{real depth}}{\text{apparent depth}}\$Substituting, \$\dfrac{4}{3}=\dfrac{12}{apparent depth}\$Therefore, \$apparent \ depth=\dfrac{12\times3}{4}=9\$The height by which it appears to be raised is \$12-9= 3cm\$

Q: A water pond appears to be \$2.7\$ in deep. If the refractive index of water is \$4/3\$, find the actual depth of the pond.

\$RI=\dfrac{\text{real depth}}{\text{apparent depth}}\$Substituting, \$\dfrac{4}{3}=\dfrac{real \ depth}{2.7}\$Therefore, \$real \ depth=\dfrac{2.7\times4}{3}=3.6\$\$Real \ depth = 3.6 m\$

Q: The apparent depth of water in cylindrical water tank of diameter \$2 R\$ cm is reducing at the rate of \$x\ cm/minute\$ when water is being drained out at a constant rate. The amount of water drained in c.c, per minute is : ( \$\displaystyle { n }_{ 1 }\$ = refractive index of air, \$\displaystyle { n }_{ 2 }\$ = refractive index of water)

Let the apparent depth be \$= d_A\$ and real depth be \$d_R\$\$\dfrac{d_R}{d_A} = \dfrac{n_2}{n_1}\$\$d_A = \dfrac{n_1}{n_2}d_R\$\$\Delta d_A = \dfrac{n_1}{n_2}\Delta d_R\$Now , \$V = \pi R^2 d_R\$\$\Delta V = \pi R^2 \Delta d_R\$putting in above equation,\$\Delta d_A = \dfrac{n_1}{n_2} \dfrac{\Delta V}{\pi R^2} = \dfrac{n_1}{n_2}\pi R^2 x\$

Q: A bird is flying \$3\ m\$ above the surface of water. If the bird is diving vertically down with speed of \$6\ m/s\$, its apparent velocity as seen by a stationary fish underwater is :\$(\mu_{water}=\dfrac{4}{3})\$

\$\dfrac { \text{apparent speed with respect to fish} }{\text{ actual speed }} \$ \$=\dfrac {\text{ refractive index of water} }{\text{ refractive index of air }}\$refractive index of water =\$ \dfrac { 4 }{ 3 }\$refractive index of water =1actual speed =6 m/s \$ \therefore \text{apparent speed }= \dfrac { 4 }{ 3 } \times 6 = 8m/s \$

Q: A fish rising up vertically toward the surface of water with speed \$3 ms^{-1}\$ observes a bird diving down vertically towards it with speed \$9 ms^{-1}\$. The actual velocity of bird is :

Here the speed of the bird wrt to fish is \$9m/s\$wrt to stationary observer in water is \$9-3=6m/s\$Actual speed of bird is \$\dfrac{6}{\mu} =\dfrac{6}{\dfrac{4}{3}}=4.5m/s\$ option \$A\$ is correct

Q: A vessel contains water up to a height of \$20\ cm\$ and above it an oil up to another \$20\ cm\$. The refractive indices of the water and the oil are \$1.33\$ and \$1.30\$ respectively. Find the apparent depth of the vessel when viewed from above.

\$\mu\$=\$\dfrac{Real depth}{Apparent depth}\$\$h_1\$=real depth 1\$h_2\$=real depth 2h'= apparent depthh'= \$\dfrac{h_1}{\mu_1}\$+\$\dfrac{h_2}{\mu_2}\$h'= \$\dfrac{20}{1.33}\$+\$\dfrac{20}{1.30}\$= 15.03+15.38= 30.41 cm.

Q: A vessel of depth x is half filled with oil of refractive index \$\mu_2\$. The apparent depth of the vessel when viewed from above is:

As refractive index, \$\mu \, = \, \dfrac{Real \, depth}{Apparent \, depth}\$\$\therefore\$ Apparent depth of the vessel when viewed from above is\$d_{apparent} \, = \, \dfrac{x}{2\mu_1} \, + \, \dfrac{x}{2\mu2}\$\$= \, \dfrac{x}{2} \, \left (\dfrac{1}{\mu_1} \, + \, \dfrac{1}{\mu_2} \right )\$\$=\, \dfrac{x}{2} \, \left(\dfrac{\mu_2 \, + \, \mu_1}{\mu_1\mu_2} \right ) \, = \, \dfrac{x(\mu_1 \, + \, \mu_2)}{2\mu_1\mu_2}\$

Question 1

A coin is placed at the bottom of a beaker containing water (refractive index $= 4/3$) to a depth of $12 cm$. By what height the coin appears to be raised when seen from vertically above?

Accepted Answer

$ RI=\dfrac{\text{real depth}}{\text{apparent depth}}$Substituting, $\dfrac{4}{3}=\dfrac{12}{apparent depth}$Therefore, $apparent  \ depth=\dfrac{12\times3}{4}=9$The height by which it appears to be raised is $12-9= 3cm$

Question 2

A water pond appears to be $2.7$ in deep. If the refractive index of water is $4/3$, find the actual depth of the pond.

Accepted Answer

$RI=\dfrac{\text{real depth}}{\text{apparent depth}}$Substituting, $\dfrac{4}{3}=\dfrac{real \  depth}{2.7}$Therefore, $real \ depth=\dfrac{2.7\times4}{3}=3.6$$Real  \ depth = 3.6 m$

Question 3

A fisherman is standing on the bank of a lake. To a fish underwater viewing obliquely the man looks:

Accepted Answer

As shown in the diagram,The due to the refraction of the light, the light will move away from the normal (NN') and consequently, the fish (denoted as F) will see a longer image of the fisherman (AB) as AB'.

Question 4

The apparent depth of water in cylindrical water tank of diameter $2 R$ cm is reducing at the rate of $x\ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in c.c, per minute is : ( $\displaystyle { n }_{ 1 }$ = refractive index of air, $\displaystyle { n }_{ 2 }$  = refractive index of water)

Accepted Answer

Let the apparent depth be $= d_A$  and real depth be $d_R$$\dfrac{d_R}{d_A} = \dfrac{n_2}{n_1}$$d_A = \dfrac{n_1}{n_2}d_R$$\Delta d_A = \dfrac{n_1}{n_2}\Delta d_R$Now , $V = \pi R^2 d_R$$\Delta V = \pi R^2 \Delta d_R$putting in above equation,$\Delta d_A = \dfrac{n_1}{n_2} \dfrac{\Delta V}{\pi R^2} = \dfrac{n_1}{n_2}\pi R^2 x$

Question 5

A bird is flying $3\ m$ above the surface of water. If the bird is diving vertically down with speed of $6\ m/s$, its apparent velocity as seen by a stationary fish underwater is :$(\mu_{water}=\dfrac{4}{3})$

Accepted Answer

$\dfrac { \text{apparent speed with respect to fish} }{\text{ actual speed }} $  $=\dfrac {\text{ refractive index of  water} }{\text{ refractive index of air }}$refractive index of water =$ \dfrac { 4 }{ 3 }$refractive index of water =1actual speed =6 m/s $ \therefore  \text{apparent speed }=  \dfrac { 4 }{ 3 } \times 6 = 8m/s $

Question 6

A fish is rising up vertically inside a pond with a velocity of 4 cm/sec and notices a bird that is diving vertically downwards towards the pond and its velocity appears to be 20 cm/sec to the fish. What is the real velocity of the diving bird, if the refractive index of water is $\dfrac{4}{3}$?

Accepted Answer

If at any instant the fish is at a distance x from the bottom surface while the bird is at a height h above the surface. Then the apparent height of the bird from surface as seen by fish is given by $\mu y$.Total apparent distance as seen by the fish at a depth x below water$h = x + \mu y$Differentiating with respect to time$\dfrac{dh}{dt}=\dfrac{dx}{dt}+\mu \frac{dy}{dt}$$20=4+\dfrac{4}{3}\cdot \dfrac{dy}{dt}$$\dfrac{16}{\dfrac{4}{3}}=\dfrac{dy}{dt}$$\therefore$ actual velocity of the diving bird = $\dfrac{48}{4}$ = $12$ cm/sec

Question 7

A fish rising up vertically toward the surface of water with speed $3 ms^{-1}$ observes a bird diving down vertically towards it with speed $9 ms^{-1}$. The actual velocity of bird is :

Accepted Answer

Here the speed of the bird wrt to fish is $9m/s$wrt to stationary observer in water is $9-3=6m/s$Actual speed of bird is $\dfrac{6}{\mu} =\dfrac{6}{\dfrac{4}{3}}=4.5m/s$ option $A$ is correct

Question 8

A vessel contains water up to a height of $20\ cm$ and above it an oil up to another $20\ cm$. The refractive indices of the water and the oil are $1.33$ and $1.30$ respectively. Find the apparent depth of the vessel when viewed from above.

Accepted Answer

$\mu$=$\dfrac{Real depth}{Apparent  depth}$$h_1$=real depth 1$h_2$=real depth 2h'= apparent depthh'= $\dfrac{h_1}{\mu_1}$+$\dfrac{h_2}{\mu_2}$h'= $\dfrac{20}{1.33}$+$\dfrac{20}{1.30}$= 15.03+15.38= 30.41 cm.

Question 9

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

Accepted Answer

As refractive index, $\mu \, = \, \dfrac{Real \, depth}{Apparent \, depth}$$\therefore$ Apparent depth  of the vessel when viewed from above is$d_{apparent} \,  = \, \dfrac{x}{2\mu_1} \, + \, \dfrac{x}{2\mu2}$$= \, \dfrac{x}{2} \, \left (\dfrac{1}{\mu_1} \, + \, \dfrac{1}{\mu_2} \right )$$=\, \dfrac{x}{2} \, \left(\dfrac{\mu_2 \, + \, \mu_1}{\mu_1\mu_2} \right ) \, = \, \dfrac{x(\mu_1 \, + \, \mu_2)}{2\mu_1\mu_2}$

Question 10

An object in a denser medium when viewed from a rarer medium appears to be raised. The shift is maximum for :

Accepted Answer

An object in a denser medium when viewed from a rarer medium appears to be raised. This is due to refraction.The dispersion of white light into a spectrum occurs because the different colors are refracted by different amounts by the water medium. Violet light is refracted most by the medium and red light is refracted least. Below is the diagrammatic representation.

Revise with Concepts

Apparent Depth

Quick Summary With Stories

Normal Shift using Glass Slab

A coin is placed at the bottom of a beaker containing water (refractive index $= 4 / 3$ ) to a depth of $12 c m$ . By what height the coin appears to be raised when seen from vertically above?

A water pond appears to be $2.7$ in deep. If the refractive index of water is $4 / 3$ , find the actual depth of the pond.

A fisherman is standing on the bank of a lake. To a fish underwater viewing obliquely the man looks:

A bird is flying $3 m$ above the surface of water. If the bird is diving vertically down with speed of $6 m / s$ , its apparent velocity as seen by a stationary fish underwater is :
$(μ_{w a t e r} = \frac{4}{3})$

A fish is rising up vertically inside a pond with a velocity of 4 cm/sec and notices a bird that is diving vertically downwards towards the pond and its velocity appears to be 20 cm/sec to the fish. What is the real velocity of the diving bird, if the refractive index of water is $\frac{4}{3}$ ?

A fish rising up vertically toward the surface of water with speed $3 m s^{- 1}$ observes a bird diving down vertically towards it with speed $9 m s^{- 1}$ . The actual velocity of bird is :

A vessel contains water up to a height of $20 c m$ and above it an oil up to another $20 c m$ . The refractive indices of the water and the oil are $1.33$ and $1.30$ respectively. Find the apparent depth of the vessel when viewed from above.

A vessel of depth x is half filled with oil of refractive index $μ_{2}$ . The apparent depth of the vessel when viewed from above is:

An object in a denser medium when viewed from a rarer medium appears to be raised. The shift is maximum for :

Revise with Concepts

Apparent Depth

Quick Summary With Stories

Normal Shift using Glass Slab

A coin is placed at the bottom of a beaker containing water (refractive index =4/3) to a depth of 12cm. By what height the coin appears to be raised when seen from vertically above?

A water pond appears to be 2.7 in deep. If the refractive index of water is 4/3, find the actual depth of the pond.

A fisherman is standing on the bank of a lake. To a fish underwater viewing obliquely the man looks:

The apparent depth of water in cylindrical water tank of diameter 2R cm is reducing at the rate of x cm/minute when water is being drained out at a constant rate. The amount of water drained in c.c, per minute is : ( n1​ = refractive index of air, n2​ = refractive index of water)

A bird is flying 3 m above the surface of water. If the bird is diving vertically down with speed of 6 m/s, its apparent velocity as seen by a stationary fish underwater is : (μwater​=34​)

A fish is rising up vertically inside a pond with a velocity of 4 cm/sec and notices a bird that is diving vertically downwards towards the pond and its velocity appears to be 20 cm/sec to the fish. What is the real velocity of the diving bird, if the refractive index of water is 34​?

A fish rising up vertically toward the surface of water with speed 3ms−1 observes a bird diving down vertically towards it with speed 9ms−1. The actual velocity of bird is :

A vessel contains water up to a height of 20 cm and above it an oil up to another 20 cm. The refractive indices of the water and the oil are 1.33 and 1.30 respectively. Find the apparent depth of the vessel when viewed from above.

A vessel of depth x is half filled with oil of refractive index μ2​. The apparent depth of the vessel when viewed from above is:

An object in a denser medium when viewed from a rarer medium appears to be raised. The shift is maximum for :

A coin is placed at the bottom of a beaker containing water (refractive index $= 4 / 3$ ) to a depth of $12 c m$ . By what height the coin appears to be raised when seen from vertically above?

A water pond appears to be $2.7$ in deep. If the refractive index of water is $4 / 3$ , find the actual depth of the pond.

A bird is flying $3 m$ above the surface of water. If the bird is diving vertically down with speed of $6 m / s$ , its apparent velocity as seen by a stationary fish underwater is :
$(μ_{w a t e r} = \frac{4}{3})$

A fish is rising up vertically inside a pond with a velocity of 4 cm/sec and notices a bird that is diving vertically downwards towards the pond and its velocity appears to be 20 cm/sec to the fish. What is the real velocity of the diving bird, if the refractive index of water is $\frac{4}{3}$ ?

A fish rising up vertically toward the surface of water with speed $3 m s^{- 1}$ observes a bird diving down vertically towards it with speed $9 m s^{- 1}$ . The actual velocity of bird is :

A vessel contains water up to a height of $20 c m$ and above it an oil up to another $20 c m$ . The refractive indices of the water and the oil are $1.33$ and $1.30$ respectively. Find the apparent depth of the vessel when viewed from above.

A vessel of depth x is half filled with oil of refractive index $μ_{2}$ . The apparent depth of the vessel when viewed from above is: