Image Shift in a Glass Slab

Q. The radius of curvature of curved surface of a plano-convex lens is $15\text{cm}$. The refractive index of the lens material is $1.5$. The focal length of plano-convex lens is (surroundings is air)

1. $20\text{cm}$
2. $-40\text{cm}$
3. $30\text{cm}$
4. $25\text{cm}$

Q. A ray PQ incident normally on the refracting face BA is refracted in the prism BAC made of material of refractive index 1.5. Complete the path of ray through the prism. From which face will the ray emerge? Justify your answer.

Q. A thin prism of angle $6^{\circ }$ made of glass of refractive index $1.5$ is combined with another thin prism made of glass of refractive index $1.75$ to produce dispersion without deviation. The angle of the second prism is :

1. $7^{\circ }$
2. $4^{\circ }$
3. $9^{\circ }$
4. $5^{\circ }$

Q. Refractive index of violet, yellow and red color of light for a material of lens are $1.66,1.64$ and $1.62$ respectively. If mean focal length of lens is $10\text{cm}$. Then chromatic aberration between the color of viole and red will be

1. $0.625\text{cm}$
2. $0.125\text{cm}$
3. $0.02\text{cm}$
4. $0.025\text{cm}$

Q. The thickness of a glass slab of refractive index 3.5 is 1 cm. The shift in the object when looked through the slab is .

1. 1.5 cm
2. 2 cm
3. 2.5 cm
4. 3 cm

Q.

A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 36 km/h. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. Take g = $10m/s^2$.

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

1. $1.532$
2. $1.732$
3. None
4. $1.414$

Q.

The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary?

Q.

A concave mirror of radius R is kept on a horizontal table. Water (refractive index $=\mu$) is poured into it up to a height h. Where should an object be placed so that its image is formed on itself ?

Q. A plane mirror is made of glass slab $({\mu }_g=1.5)$ 2.5 cm
Thick and silvered on back. A point object is placed 5 cm in front of the unsilvered face of the mirror. What be the position of final image?

1. 12.5 cm from unsilvered face
2. 5.67 cm from unsilvered face
3. 14.6 cm from unsilvered face
4. 8.33 cm from unsilvered face

Q.

An object is placed at distance of 10 cm in air from the front surface of a thick glass slab of thickness 6 cm whose back surface has been silvered and is placed in air. The image is formed at a distance of 14 cm from the polished surface. The refractive index of the material of the thick mirror is

1. 1.2
2. 1.3
3. 1.4
4. 1.5

Q. For the lens arrangement shown in the figure, The effective focal length is $-60\text{m}$. The radii of curvature of the curved surfaces of plano-convex lenses are $12\text{cm}$ each and refractive index of the material of the lens is $1.5$. Find the refractive index of the liquid.

1. $1.33$
2. $1.42$
3. $1.53$
4. $1.60$

Q. Rays from a lens are converging toward a point $P$ as shown in figure. How much thick glass plate having refractive index $1.6$ must be located between the lens and point $P$, so that the image will be formed at $P$’?

1. $0.8cm$
2. $1.6cm$
3. $0.8cm$
4. $2.4cm$

Q. If both the lenses used for achromatic are of same material, then

1. Chromatic is removed
2. Chromatic cannot be removed
3. Data insufficient
4. None of these

Q. Consider the refraction of light ray as shown in the figure below. Incident ray is rotating with constant angular velocity 2 rad/sec. What is the angular velocity of refracted ray, when the angle of incidence becomes ${30}^{\circ }$? (Given $\frac{n_1}{n_2}=\sqrt{3}$)

1. 2 rad/s
2. 6 rad/s
3. $\sqrt{3}$ rad/s
4. $\frac{1}{2}$ rad/s

Q. A slab of transparent material is made as shown in the figure. The thickness of $C$ is twice the thickness of $B$. If the number of waves in $A$ is equal to the number of waves in combination of $B$ and $C$, then the refractive index of $B$ is

1. $1.8$
2. $1.6$
3. $1.4$
4. $1.33$

Q. In Young's double-slit arrangement, water is filled in the space between screen and slits. Then -

1. 
   
   fringe pattern shifts upwards, but fringe width remains unchanged
2. 
   
   fringe width decreases, and central bright fringe shifts upwards
3. 
   fringe width increases, and central bright fringe does not shift
4. 
   fringe width decreases, and central bright fringe does not shift

Q. Consider an equiconvex lens of radius of curvature R and focal length f. If f > R, the refractive index $\mu$ of the material of the lens.

1. is greater than zero but less than 1.5
2. is greater than 1.5 but lens than 2.0
3. is greater than 1.0 but less than 1.5
4. none of these

Q. As shown in figure, light is incident normally on one face of the prism. A liquid of refractive index $\mu$ is placed on the horizontal face $\text{AC}$. The refractive index of prism is $3/2$. If total internal reflection taken place on face $\text{AC}$, $\mu$ should be less than $\frac{l\sqrt{3}}{4},$ where $l$ is an integer. Find the value of $l$.

Q. Two transparent media $\text{A}$ & $\text{B}$ having refractive indices ${\mu }_A=1.5$ and ${\mu }_B=1.2$ respectively in an optical fibre are seperated by a plane boundary. The speed of light in medium $\text{A}$ is $2\times {10}^3\text{m/s}$ and in medium $B$ is $2.5\times {10}^3\text{m/s}$. The critical angle for which a ray of light going from $\text{A}$ to $\text{B}$ is totally internally reflected is :-

1. 
   ${\sin }^{-1}\left(\frac{1}{2}\right)$
2. 
   ${\sin }^{-1}\left(\frac{2}{5}\right)$
3. 
   ${\sin }^{-1}\left(\frac{4}{5}\right)$
4. 
   ${\sin }^{-1}\left(\frac{1}{3}\right)$

Q.

The speed of light in a transparent medium is $2.44\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Find the refractive index of the medium?

Q. The thickness of a glass slab of refractive index 3.5 is 1 cm. The shift in the object when looked through the slab is .

1. 1.5 cm
2. 2 cm
3. 2.5 cm
4. 3 cm

Q. Focal length of a lens depends on the
(a) Medium constituting lens only.
(b) Medium constituting the surroundings only.
(c) Medium constituting the lens as well as surroundings.
(d) Wavelength of incident light.

1. only (a)
2. (a) and (d) both.
3. (c) and (d) both
4. only (b)

Q. An object is placed in front of a slab $(\mu =1.5)$ of thickness $6\text{cm}$ at a distance of $28\text{cm}$ from it, while the other face of the slab is silvered. Find the position of the final image.

1. $36\text{cm}$ from surface $1$
2. $54\text{cm}$ from surface $2$
3. $36\text{cm}$ from surface $2$
4. $54\text{cm}$ from surface $1$

Q. For the given incident ray as shown in figure, the condition of total internal reflection of the ray will be satisfied, if the refractive index of block will b

Q. A thin, symmetric double convex lens of power $P$ is cut into three parts $\text{A, B}$ and $\text{C}$ as shown in figure.


Which of the following options is correct regarding the power of parts of lens?

1. Power of part $\text{A}$ is $2P$
2. Power of part $\text{B}$ is $2P$
3. Power of part $\text{B}$ is $\frac{P}{2}$
4. Power of part $\text{C}$ is $\frac{P}{4}$

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

Q. An equilateral prism has refractive index as 1.5. The angle of deviation of the ray is 10n degrees, if a ray is incident normally on a surface. Find n.

Q. An object is placed in front of a slab $(\mu =1.5)$ of thickness $6\text{cm}$ at a distance of $28\text{cm}$ from it, while the other face of the slab is silvered. Find the position of the final image.

1. $54\text{cm}$ from surface $1$
2. $36\text{cm}$ from surface $2$
3. $36\text{cm}$ from surface $1$
4. $54\text{cm}$ from surface $2$

Q. There is a small source of light at some depth below the surface of water (refractive index $=4/3$) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and the absorption by water, percentage of light that emerges out of surface is (nearly):
[Use the fact that surface area of a spherical cap of height $h$ and radius of curvature $r$ is $2\pi rh$]

1. $50\%$
2. $21\%$
3. $17\%$
4. $34\%$