Apparent Depth

Q. Famous relation in physics relates ${}^{\prime }{\text{moving mass}}^{\prime }m$ to the ${}^{\prime }{\text{rest mass}}^{\prime }{m}_{\circ }$ of a particle in terms of its speed $v$ and the speed of light, $c$. (This relation first arose as a consequence of special theory of relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant $c$. He writes:

$m=\frac{m_{\circ }}{(1-v^2{)}^{\frac{1}{2}}}$

Guess Where to put the missing $c$.

Q.

Monochromatic light is refracted from air into glass of refractive index $\mu$. The ratio of the wavelengths of incident and refracted waves is

1. $\mu :1$
2. $1:{\mu }^2$
3. $1:\mu$
4. ${\mu }^2:1$

Q. A ray of light passing through a prism $(\mu =\sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is (in degrees)

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. None of these

3. 15 cm

4. 6.67 cm

Q. 133.a ball is drop from height of 20m above surface of water in lake. Refractive index of water is 4/3.A fish inside lake, in line of fall of ball, is looking at ball.At an instant, when ball is 12.8m above water surface , the fish see speed of ball as

Q. Consider the situation shown in figure, water $({\mu }_w=4/3)$ is filled in a beaker up to a height of $10\text{cm}$. A plane mirror fixed at a height of $5\text{cm}$ 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. $15\text{cm}$
2. $12.5\text{cm}$
3. $7.5\text{cm}$
4. $10\text{cm}$

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

Q. Number of particles is given by $n=D\frac{n_2-h_1}{x_2-x_1}$ crossing a unit area perpendicular to $X-\text{axis}$ in unit time, when $n_1$ and $n_2$ are number of particles per unit volume for the value of $x$ meant to $x_2$ and $x_1$. Find dimension of $D$ called as diffusion constant.

1. $\left[M^{0}L{T}^2\right]$
2. $\left[M^{0}L{T}^{-3}\right]$
3. $\left[M^0{L}^2{T}^{-1}\right]$
4. $\left[M^0{L}^2{T}^{-4}\right]$

Q. A glass slab $(\mu =1.5)$ of thickness $2\text{cm}$ is placed on a spot. The shift of spot if it is viewed from top will be

1. $\frac{2}{3}\text{cm}$
2. $\frac{4}{3}\text{cm}$
3. $\frac{5}{3}\text{cm}$
4. $\frac{7}{3}\text{cm}$

Q. A light ray enters a solid glass sphere of refractive index $\mu =\sqrt{3}$ at an angle of incidence ${60}^{\circ }$. The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the reflected and refracted rays at this surface is

Q.

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

1. 2.5

2. 1.5

3. 1.6

4. 2

Q. A mark at the bottom of a liquid container appears to rise by $0.1\text{m}$ when viewed from above. The depth of the liquid is $1\text{m}$. Then, the refractive index of the liquid is :

1. $1.33$
2. $\frac{9}{10}$
3. $\frac{10}{9}$
4. $1.5$

Q. A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1\text{cm}$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\times {10}^{-6}\text{m}$

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. When monochromatic light travel from a rare to denser medium explain the following is frequency of reflected and refracted light same as incident light does decrease in speed imply a reduction in energy carried by light wave

Q.

The Refractive index of diamond with respect to glass is $1.6$ and the absolute refractive index of glass is $1.5$. Find out the absolute refractive index of a diamond.

Q.

Three glass cylinders of equal height $H=30cm$ and same refractive index $n=1.5$ are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3 m ). If $H_1,H_2$ and $H_3$ are the apparent depths of a point X on the bottom of the three cylinders respectively, the correct statement(s) is/are

1. $H_2>H_1$

2. $H_3>H_1$

3. $0.8cm<(H_2-H_1)<0.9cm$

4. $H_2>H_3$

Q. 8.An under water swimmer is at a depth of 12m below the surface of water.A bird is height of 18m from the surface of water directly above of his eyes.for the swimmer the birds appear at the distance from the surface of water is equal to the( refractive index of water is 4/3)

Q. A diffraction grating is ruled with $600$ lines per $mm$. When monochromatic light falls normally on the grating, the first order diffracted beams are observed on the far side of the grating each making an angle ${15}^{\circ }$ with the normal to grating. What is the frequency of the light? (Given $\sin {15}^{\circ }=0.258$)

1. $1.2\times {10}^{13}Hz$
2. $7.0\times {10}^{14}Hz$
3. $4.7\times {10}^{13}Hz$
4. $1.9\times {10}^{14}Hz$

Q. When a light ray from a rarer medium is refracted into a denser medium, its

1. Speed increases, wavelength increases
2. Speed decreases, wavelength increases
3. Speed increases, wavelength decreases
4. Speed decreases, wavelength decreases

Q. A point object is placed in front of a 5 cm thick plane glass mirror. Find the location of final image with respect to object.

1. $\frac{35}{3}cm$
2. 15 cm
3. $\frac{40}{3}cm$
4. $\frac{80}{3}cm$

Q. A fish is moving up vertically with speed 4 cm/s inside a pond. A bird is moving vertically downward (see figure). Velocity of the bird w.r.t. fish is 16 cm/s downward. Find out the actual velocity of the bird (in cm/s). Given refractive index of water is $\frac{4}{3}$.

Q. Find the apparent depth and apparent shift of an object placed at the bottom of the a vessel containing a glass slab of thickness 10 cm and water of height 50 cm. as shown in the figure.

1. 30 cm
2. 40 cm
3. 20 cm
4. 25 cm

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

Q. For the following assertion $\left(A\right)$ and reason $\left(R\right)$, choose the correct option.
$A:$ The apparent depth of a tank of water decreases if viewed from near normal incidence.
$R:$ Real depth decreases if viewed obliquely.

1. Both assertion and reason are true and reason is a correct explanation of assertion
2. Both assertion and reason are true and reason is not a correct explanation of assertion
3. Assertion is true, but reason is false
4. Assertion is false, but reason is true

Q. A bird in air is diving vertically downwards over a tank, with speed $5\text{cm/s}$, while the base of the tank is silvered. A fish in the tank is rising upwards along the same line with a speed $2\text{cm/s}$. Water level is falling at the rate of $2\text{cm/s}$. Then:
[Take ${\mu }_{water}=4/3$]

1. Speed of the image of the fish as seen by the bird directly is $6\text{cm/s}$.
2. Speed of the image of the fish as seen by the bird directly is $3\text{cm/s}$.
3. Speed of the image of the fish as seen by the bird after reflection from the mirror is $3\text{cm/s}$.
4. Speed of the image of the fish as seen by the bird after reflection from the mirror is $6\text{cm/s}$.

Q. A concave mirror is placed inside water with its shining surface upward and principal axis vertical as shown in the figure. The final position of the image from the interface seen by an observer above interface if incident ray strikes normal to interface will be

1. $7.5\text{cm}$ below the interface
2. $7.5\text{cm}$ above the interface
3. $9.5\text{cm}$ below the interface
4. $9.5\text{cm}$ above the interface

Q.

The refracting angle of a prism is $A$ and the refractive index of the material of the prism is $cot\left(\frac{A}{2}\right)$. The angle of minimum deviation is

1. $180°-2A$

2. $90°-2A$

3. $180°+2A$

4. $180°-3A$

Q.

An object P is focussed by a microscope M. A glass slab of thickness 2.1 cm is introduced between P and M. If the refractive index of the slab is 1.5, by what distance should the microscope be shifted to focus the object again ?