Combination of Spherical Mirrors

Q. A converging mirror M1, a point source S and a diverging mirror M2 are arranged as shown in fig. The source is placed at a distance of 30 cm from M1. The focal length of each of the mirrors is 20 cm. Consider only the images formed by a maximum of two reflections. It is found that one image is formed on the source itself. Find the distance between the two mirrors.

1. 30 cm
2. 40 cm
3. 50 cm
4. 60 cm

Q.

In a concave mirror experiment, an object is placed at a distance $x_1$ from the focus and the image is formed at a distance $x_2$ from the focus. The focal length of the mirror would be

1. $\sqrt{2x_1{x}_2}$
2. $\sqrt{x_1{x}_2}$
3. $\sqrt{\frac{x_1^2}{x_2}}$
4. $\frac{x_1+x_2}{2}$

Q. A concave mirror of focal length $10\text{cm}$ and a convex mirror of focal length $15\text{cm}$ are placed $40\text{cm}$ apart facing each other’s reflecting surface. A point object is placed between the mirror on their common axis and $15\text{cm}$ from the concave mirror. Find the position of images produced by reflection at concave mirror first and then at convex mirror.

1. $10\text{cm}$ behind the convex mirror
2. $6\text{cm}$ behind the convex mirror
3. $6\text{cm}$ infront of the convex mirror
4. $10\text{cm}$ infront of the convex mirror

Q.

Magnification produced by a rear view mirror fitted in vehicles

1. is less than one

2. is more than one

3. is equal to one

4. can be more than or less than one depending upon the position of the object in front of it

Q. In the figure shown "$O$" represents the point object. Find the coordinates of the image formed by the plane mirror .

1. $(0,-\sqrt{2})$
2. $(0,-2)$
3. $(0,2\sqrt{2})$
4. $(0,-2\sqrt{2})$

Q. An image of a candle (placed infront of a mirror) on a screen is found to be double its size. When the candle is shifted by a distance $5\text{cm}$, then the image becomes triple its size. Find the radius of curvature (in decimeter) of the mirror.

Q. A point source S is placed midway between two converging mirrors having equal focal length f as shown in fig. Find the values of d for which only one image is formed.

1. 2f, 3f
2. 3f, 4f
3. f, 2f
4. 2f, 4f

Q.

When an object is placed in front of a concave mirror at a distance $30\mathrm{cm}$ an image is obtained on a screen at a distance of $20\mathrm{cm}$ from the mirror. Find the focal length of the mirror.

Q. Find the length of field of view on $\text{Y}$-axis when the object is at $\text{A}$ $\text{(2, 0)}$ and $\text{MN}$ is a plane mirror as shown in the figure below.

Q. A reflecting surface is represented by the equation $x^2+y^2=a^2$. A ray travelling in negative x-direction is deviated towards positive y-direction after reflection from the surface at point $P$. Then co-ordinates of point $P$ are

1. $(0.8a,0.6a)$
2. $(0.6a,0.8a)$
3. None of these
4. $(\frac{a}{2},\frac{a}{2})$

Q. A concave and a convex mirror of focal lengths $10\text{cm}$ each are placed at a distance $d\text{cm}$ apart. An object $\text{AB}$ is placed in between the mirrors at a distance of $10\text{cm}$ from the convex mirror. If first ray is incident on the convex mirror and then on the concave mirror then find the distance $d$ between both the mirrors, so that final image will be formed at the object's position.

1. $10\text{cm}$
2. $15\text{cm}$
3. $20\text{cm}$
4. $25\text{cm}$

Q. A plane mirror is placed along positive $x-$ axis facing along the positive $y-$ axis. The equation of a linear object is $x=y$. The equation of its image is

1. $x=y$
2. $x+y=0$
3. $2x+y=0$
4. None of these

Q. Find out the distance of the point where the incident ray intersects the principal axis from the pole of the mirror.

1. $\frac{15}{2}\text{cm}$
2. $\frac{15}{8}\text{cm}$
3. $\frac{15}{4}\text{cm}$
4. $\frac{25}{4}\text{cm}$

Q.

What is the focal length of a plane mirror

1. 2F

2. F

3. Infinite

4. 3F

Q.

Magnification produced by a rear view mirror fitted in vehicles is?

Q. Assertion :When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{max}$ increase. Reason: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. An object is placed at a distance of $40cm$ from a concave mirror of focal length $15cm$. If the object is displaced through a distance of $20cm$ towards the mirror, the displacement of the image will be:

1. $30cm$ towards the mirror
2. $30cm$ away from the mirror
3. $36cm$ towards the mirror
4. $36cm$ away from the mirror

Q. An object is placed symetrically between the two perpendicular plane mirrors as shown in the figure. The equation of the locus of all the images formed by this arrangement is

[Assume the intersection point of the mirrors as the origin.]

1. $x+y=a$
2. $(x-a{)}^2+(y-a{)}^2=a^2$
3. $(x-a{)}^2+ax-a=0$
4. $x^2+y^2=2a^2$

Q. In figure find the total magnification after two successive reflections first on $M_1$ and then on $M_2$.

1. + 1
2. - 2
3. - 1
4. + 2

Q. A concave mirror of focal length $10\text{cm}$ and a convex mirror of focal length $15\text{cm}$ are placed facing each other $40\text{cm}$ apart. A point object is placed between the mirrors on their common axis and $15\text{cm}$ from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.

1. $12\text{cm}$ behind convex mirror, real
2. $9\text{cm}$ behind convex mirror, real
3. $6\text{cm}$ behind convex mirror, virtual
4. $3\text{cm}$ behind convex mirror, virtual

Q. Find the nature of image when an object is placed at $2f$ from the pole of a convex mirror of focal length $f$

1. Virtual, erect and $3$ times
2. Real, inverted and $\frac{1}{3}$ times
3. Real, inverted and of same size
4. Virtual, erect and of $\frac{1}{3}$ times

Q. Use the mirror equation to show that an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.

Q. A point source is placed at co-ordinates $(0,1)$ in X-Y plane. A ray of light from the source is reflected on a plane along the X-axis and perpendicular to the X-Y plane. The reflected ray passes through the point $(3,3)$. What is the path length of the ray from $(0,1)$ to $(3,3)$?

1. $\sqrt{13}$
2. $5$
3. $2\sqrt{13}$
4. $1+2\sqrt{3}$

Q. A converging mirror M1, a point source S and a diverging mirror M2 are arranged as shown in fig. The source is placed at a distance of 30 cm from M1. The focal length of each of the mirrors is 20 cm. Consider only the images formed by a maximum of two reflections. It is found that one image is formed on the source itself. Find the distance between the two mirrors.

1. 30 cm
2. 40 cm
3. 50 cm
4. 60 cm

Q. Two plane mirrors of length $L$ are separated by distance $L$ and a man $M_2$ is standing at distance $L$ from the connecting line of mirrors as shown in figure. A man $M_1$ is walking in a straight line at distance $2L$ parallel to mirrors at speed $U$. The time for which man $M_2$ at O will be able to see image of $M_1$ is

1. $\frac{8L}{U}$
2. $\frac{3L}{U}$
3. $\frac{6L}{U}$
4. $\frac{nL}{U}$

Q.

what is radius of curvature and centre of curvature of a mirror

Q. A point light source is kept in front of a convex mirror ata distance of $40cm$. The focal length of the mirror is $40cm$. Find the position of image.

Q. A concave mirror of focal length $10\text{cm}$ and an convex mirror of focal length $15\text{cm}$ are placed facing each other $40\text{cm}$ apart. A point object is placed between the mirrors, on their common axis and $15\text{cm}$ from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.

1. $12\text{cm}$ behind convex mirror, real
2. $9\text{cm}$ behind convex mirror, real
3. $6\text{cm}$ behind convex mirror, virtual
4. $3\text{cm}$ behind convex mirror, virtual

Q. A radiation of energy 'E' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (C=Velocity of light)

1. $\frac{2E}{C^2}$
2. $\frac{E}{C}$
3. $\frac{E}{C^2}$
4. $\frac{2E}{C}$

Q. A $1cm$ object is placed perpendicular to the principal axis of a convex mirror of focal length $7.5cm$ . Find its distance from the mirror if the image formed is $0.6cm$ in size.