3D Image Formation by Lenses and Mirrors

Q. A point object is placed at a distance $12\text{cm}$ from a convex lens of focal length $10\text{cm}$. On the other side of the lens, a convex mirror is placed at a distance of $10\text{cm}$ from the lens such that the image formed by the combination coincides with the object itself. The focal length of the convex mirror is

1. $20\text{cm}$
2. $25\text{cm}$
3. $30\text{cm}$
4. $35\text{cm}$

Q. The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea $7.8\text{mm}$. This surface separates two media of refractive indices $1$ and $1.34$. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

1. $1\text{cm}$
2. $2\text{cm}$
3. $4.0\text{cm}$
4. $3.1\text{cm}$

Q. A convex lens of focal length 20 cm is placed coaxially with a concave mirror of focal length 10 cm, at a distance 50 cm apart from each other. A beam of light coming parallel to the principal axis is incident on the convex lens. Find the position of the final image formed by this combination. Draw the ray diagram showing the formation of the image.

Q.

A converging lens of focal length 15 cm and a converging mirror of focal length 10 cm are placed 50 cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens. Find the locations of the two images formed.

Q.

A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis ?

Q. An object is placed at $O$ and the image obtained at $O^{\prime }$ as shown below.


If the refractive index of glass slab is $1.5$, then the thickness of the slab is

1. $3\text{cm}$
2. $6\text{cm}$
3. $9\text{cm}$
4. $12\text{cm}$

Q.

A converging lens of focal length 15 cm and a converging mirror of focal length 20 cm are placed with their principal axes coinciding. A point source S is placed on the principal axis at a distance of 12 cm from the lens as shown in figure It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.

1. 20 cm

2. 40 cm

3. 60 cm

4. 80 cm

Q.

An object is placed in front of a convex mirror at a distance equal to the focal length of the mirror. If its focal length is $20cm$ , the distance of the image from the mirror is ……cm.

1. $10$

2. $20$

3. $40$

4. infinity

Q.

A converging lens and a diverging mirror are placed at a separation of $20\text{cm}$. The focal length of the lens is $30\text{cm}$ and that of the mirror is $50\text{cm}$ . Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?

1. $17.5\text{cm}$ from lens
2. $2.5\text{cm}$ from lens
3. $10\text{cm}$ from mirror
4. $19.5\text{cm}$ from lens

Q. A concave refracting surface of a medium having refractive index $\mu$ produces a real image of an object (located outside the medium) irrespective of its location

1. always
   
2. may be if refractive index of surrounding medium is greater than 1.
3. may be if refractive index of surrounding medium is less than $\mu$
4. none of the above

Q. A thin plano-convex lens acts like concave mirror of focal length $0.2m$ when silvered at its plane surface. Refractive index of the material of lens is $1.5$. Radius of curvature of convex surface of the lens is

1. $0.1m$
2. $0.2m$
3. $0.4m$
4. $0.8m$

Q.

A converging lens of focal length$20cm$ is placed between an object and a concave mirror of focal length $10cm$ as shown in figure. The final image is

1. Coinciding with object, enlarged, Inverted real

2. Coinciding with object, same size, erect, real

3. Coinciding with object, same size, Inverted, Vertical

4. Coinciding with object, same size, Inverted, real

Q.

A thin equiconvex lens of glass $(\mu =\frac{3}{2})$ having a focal length of 30 cm in air is placed at a distance of 10 cm from a plane mirror, which, in turn is placed with its plane perpendicular to the optic axis of the lens. Water $(\mu =\frac{4}{3})$ fills the space between lens and mirror. A parallel beam of light is incident on the lens parallel to the principal axis. Choose the correct option(s):

1. Final image is 18 cm left to the lens.

2. Final image is 18 cm right to the lens.

3. If mirror is rotated by $1^{\circ }$, as shown in figure, final image is displaced by \(\frac{\pi}{3}~cm\).

4. If mirror is rotated by $1^{\circ }$, as shown in figure, final image is displaced by \(\frac{5 \pi}{9}~cm\).

Q. A point source of light is placed at 2f from a converging lens of focal length f. A flat mirror is placed on the other side of the lens at a distance d from lens such that rays reflected from the mirror are parallel after passing through the lens again. If f=30 cm, then d is equal to

1. 15 cm
2. 30 cm
3. 45 cm
4. 75 cm

Q. A convex mirror of focal length $10cm$ is placed in water. The refractive index of water is $\frac{4}{3}$. What will be the focal length of the mirror in water.

1. $10cm$
2. $\frac{40}{3}cm$
3. None of these
4. $\frac{30}{4}cm$

Q. At what distance from $O$ the image for the converging beam after refraction through the curved surface will be formed?

1. $40\text{cm}$
2. $\frac{40}{3}\text{cm}$
3. $20\text{cm}$
4. $\frac{180}{7}\text{cm}$

Q.

A converging lens of focal length 15 cm and a converging mirror of focal length 20 cm are placed with their principal axes coinciding. A point source S is placed on the principal axis at a distance of 12 cm from the lens as shown in figure It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.

1. 20 cm

2. 40 cm

3. 60 cm

4. 80 cm

Q.

A converging lens of focal length 15 cm and a converging mirror of focal length 20 cm are placed with their principal axes coinciding. A point source S is placed on the principal axis at a distance of 12 cm from the lens as shown in figure It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.

1. 20 cm

2. 40 cm

3. 60 cm

4. 80 cm

Q. A point like object is placed at a distance of $1\text{m}$ in front of a convex lens of focal length $0.5\text{m}.$ A plane mirror is placed at a distance of $2\text{m}$ behind the lens. The position and nature of the final image formed by the system is :

1. $2.6\text{m}\text{from the mirror, real}$
2. $1\text{m}\text{from the mirror, virtual}$
3. $1\text{m}\text{from the mirror, virtual}$
4. $3.66\text{m}\text{from the mirror, virtual}$

Q. An object is placed in front of a thin convex lens of focal length 30 cm and a plane mirror is placed 15 cm behind the lens. If the final image of the object coincides with the object, the distance of the object from the lens is :

1. 60 cm
2. 30 cm
3. 15 cm
4. 25 cm

Q.

A converging lens of focal length 15 cm and a converging mirror of focal length 20 cm are placed with their principal axes coinciding. A point source S is placed on the principal axis at a distance of 12 cm from the lens as shown in figure It is found that the final beam comes out parallel to the principal axis. Find the separation between the mirror and the lens.

1. 20 cm

2. 40 cm

3. 60 cm

4. 80 cm

Q. A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm.The distance from the lens a convex mirror of radius of curvature 10 cm should be placed on the other side of the lens such that the real images formed on the source itself is

1. $30cm$
2. $12cm$
3. $50cm$
4. $60cm$

Q. Assertion: Position of image approaches focus of a lens, only when object approaches infinity.
Reason: Paraxial rays incident parallel to principal axis intersect at the focus after refraction from lens.

1. Both Assertion and Reason are true and the Reason is the correct explanation of the Assertion
2. Both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion
3. Assertion is true statement but Reason is false
4. Both Assertion and Reason are false statements

Q. When an object is at a distance $u_{1}and{u}_2$ from the optical centre of a lens, a real and virtual image are formed respectively, with the same magnification. The focal length of lens is :

1. $\frac{u_1-u_2}{2}$
2. $(u_1+u_2)$
3. $u_1+\frac{u_2}{2}$
4. $\frac{u_1+u_2}{2}$

Q. At what distance from $O$ the image for the converging beam after refraction through the curved surface will be formed?

1. $40\text{cm}$
2. $\frac{40}{3}\text{cm}$
3. $20\text{cm}$
4. $\frac{180}{7}\text{cm}$

Q. A real image is formed by a convex lens. If we put a concave lens in contact with it, the combination again forms a real image. The new image :

1. Is farther from the lens system
2. Is closer to the ens system
3. Is at the origins position
4. May be anywhere depending on the focal length of the concave lens

Q. Two thin films of the same material but different thickness are separated by air. Monochromatic light in incident on the first film. When viewed normally from the point $A$, the second film appears dark.
From point $B$, on normal viewing

1. the first film will appear dark
2. the second film will appear bright
3. the first film will appear bright
4. the second film will appear dark

Q. A thin biconvex lens of refractive index $3/2$ and radius of curvature $50cm$ is placed on a reflecting convex surface of radius of curvature $100cm$. A point object is placed on the principal axis of the system such that its final image coincides with itself. Now, few drops of a transparent liquid is placed between the mirror and lens such that final image of the object is at infinity. Find refractive index of the liquid used. Also, find the position of the object.

Q. A converging lens of focal length $15cm$ and a converging mirror of focal length $10cm$ are placed $50cm$ apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of $40cm$ from the lens. Find the location of the two images formed.

Q. (a) An equiconvex lens with radii of curvature of magnitude $r$ each, is put over a liquid layer poured on top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted real image coincides with the needle itself. The distance of the needle from the lens is measured to be ${}^{\prime }{a}^{\prime }$. On removing the liquid layer and repeating the experiment the distance is found to be ${}^{\prime }{b}^{\prime }$.
Given that two values of distances measured represent the focal length values in the two cases, obtain a formula for the refractive index of the liquid.
(b) If $r=10cm,a=15cm,b=10cm$, find the refractive index of the liquid.