Apparent Depth

Q. A container has two layers of immiscible liquids $1$ and $2$ with refractive indices $1.5$ and $4/3$ respectively. What is apparent position of an object placed at the bottom of the vessel. Thickness of the layers are $3\text{cm}$ and $8\text{cm}$ respectively?

1. $6\text{cm}\text{below the liquid 2 - air interface.}$
2. $8\text{cm}\text{below the liquid 2 - air interface.}$
3. $8\text{cm}\text{below the liquid 1 - liquid 2 interface.}$
4. $6\text{cm}\text{below the water - air interface.}$

Q. How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}_a{\mu }_{\omega }=\frac{4}{3}$)

1. 8.0 cm
2. 10.5 cm
3. 12.0 cm
4. None of the above

Q. A fish lies at the bottom of a $4m$ deep water lake. A bird flies $6m$ above the water surface and refractive index of water is $\frac{4}{3}$. Then the distance between

1. Bird and image of fish is $8m$
2. Fish and image of bird is $12m$
3. Fish and image of bird is $8m$
4. Fish and image of bird is $10m$

Q. A fish is vertically below a flying bird moving vertically down towards water surface. The bird will appear to the fish to be ( assuming fish moves along the vertical joining fish and bird)

1. moving faster than its real speed and also away from the real distance.
2. moving faster than its real speed and nearer than its real distance.
3. moving slower than its real speed and also nearer than its real distance.
4. moving slower than its real speed and away from the real distance.

Q. The image of a coin kept inside water as seen from above the water surface is a

1. Virtual image
2. Real image
3. May be virtual or real image depending upon the R.I of water
4. We don’t see an image, we see the object in such a situation

Q.

An air bubble in a glass slab $(\mu =1.5)$ is 6 cm deep when viewed from one face and 4 cm deep when viewed from the opposite face. The thickness of the glass plate is3

1. 10 cm

2. 6.67 cm

3. 15 cm

4. None of these

Q. A vessel of depth 2d cm is half filled with a liquid of refractive index ${\mu }_1$ and the upper half with a liquid of refractive index ${\mu }_2$. The apparent depth of the vessel seen perpendicularly is

1. $d\left(\frac{{\mu }_1{\mu }_2}{{\mu }_1+{\mu }_2}\right)$
2. $d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
3. $2d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
4. $2d\left(\frac{1}{{\mu }_1{\mu }_2}\right)$

Q. Consider the situation as shown in figure. A plane mirror is fixed at a height $h$ above the bottom of a beaker containing water (refractive index $\mu$ ) up to a height $d$. Find the position of the image of the bottom formed by the mirror.

1. $h-d+\frac{d}{\mu }$
2. $h+d+\frac{d}{\mu }$
3. $h-d-\frac{d}{\mu }$
4. $d+\frac{d}{\mu }$

Q. A vessel of depth 2d cm is half filled with a liquid of refractive index ${\mu }_1$ and the upper half with a liquid of refractive index ${\mu }_2$. The apparent depth of the vessel seen perpendicularly is

1. $d\left(\frac{{\mu }_1{\mu }_2}{{\mu }_1+{\mu }_2}\right)$
2. $d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
3. $2d(\frac{1}{{\mu }_1}+\frac{1}{{\mu }_2})$
4. $2d\left(\frac{1}{{\mu }_1{\mu }_2}\right)$

Q.

A rectangular tank of depth 8 meter is full of water (), the bottom is seen at the depth [MP PMT 1987

1. 6 m

2. 8/3 m

3. 8 cm

4. 10 cm

Q. A transparent cube of 15 cm edge contains a small air bubble. Its apparent depth when viewed through one face is 6 cm and when viewed through the opposite face is 4 cm. Then the refractive index of the material of the cube is

1. 2
2. 2.5
3. 1.6
4. 1.5

Q.

A fish inside a river will appear at a _________ depth to an observer looking from the ground.

1. lesser

2. greater

3. exact

4. Inadequate data.

Q. A printed page is kept pressed by a glass cube ($\mu$ = 1.5) of edge 6.0 cm. By what amount will the printed letters appear to be shifted when viewed from the top?

1. 2.0 cm
2. 4.0 cm
3. 6.0 cm
4. 8.0 cm

Q. Consider the situation shown in figure. Water $({\mu }_w=\frac{4}{3})$ is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is

1. 15 cm
2. 12.5 cm
3. 7.5 cm
4. 10 cm

Q.

An air bubble in a glass slab $(\mu =1.5)$ is 6 cm deep when viewed from one face and 4 cm deep when viewed from the opposite face. The thickness of the glass plate is3

1. 10 cm

2. 6.67 cm

3. 15 cm

4. None of these

Q. A beaker contains water up to a height $h_1$ and oil above water up to another height $h_2.$ Find the apparent shift in the position of the bottom of the beaker when viewed from above. Refractive index of water is ${\mu }_1$ and that of oil is ${\mu }_2.$

1. $(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$
2. $(1-\frac{1}{{\mu }_1})h_1-(1-\frac{1}{{\mu }_2})h_2$
3. $(1-\frac{1}{{\mu }_1})h_1+(1-\frac{1}{{\mu }_2})h_2$
4. $(1-\frac{1}{{\mu }_1})h_1-(1-\frac{1}{{\mu }_2})h_2.$

Q. How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}_{\alpha }{\mu }_{\omega }=\frac{4}{3}$

1. 8.0 cm
2. 10.5 cm
3. 12.0 cm
4. None of the above