Mirror Formula Examples

Q.

An object is placed at a distance of 10 cm from a convex mirror of a focal length of 15 cm. Find the position and nature of the image.

Q.

A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of a focal length of 10 cm. The center of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is

1. 36cm²

2. 6cm²

3. 16cm²

4. 4cm²

Q.

A convex mirror of radius of curvature $20cm$ forms an image which is half the size of the object. Determine the position of the object from the pole of the mirror.

Q.

An object at a distance of 30 cm from a concave mirror gets its image at the same point. The focal length of the mirror is

1. -30 cm

2. 30 cm

3. -15 cm

4. 15 cm

Q. A linear object is placed along the axis of a mirror as shown in figure. If $f$ is the focal length of the mirror, then the length of image is

1. $\frac{2f}{3}$
2. $\frac{f}{3}$
3. $f$
4. None of these

Q.

Find the diameter of the image of the moon formed by a spherical concave mirror of focal length 7.6 m. The diameter of the moon is 3450 km and the distance between the earth and the moon is $3.8\times {10}^5\text{km}$

Q. An object is placed in front of a convex mirror at a distance of $50\text{cm}$. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is $30\text{cm}$, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?

1. $25\text{cm}$
2. $20\text{cm}$
3. $12.5\text{cm}$
4. $50\text{cm}$

Q. a real image obtained by a concave mirror is 4 times bigger than the object.If the object is displaced by 3 cm away from mirror , image size becomes 3 times the object size.find focal lenth of mirror

Q. image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 25/3m to 50/7m in 30 seconds. What is the speed objective of in km per hour

Q. 117.A concave mirror having the focal length 15 cm forms an image having twice the linear dimensions of the object if the image is virtual , then the position of the object will be

Q.

Use the mirror equation to deduce that:

(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

(b) a convex mirror always produces a virtual image independent of the location of the object.

(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.

(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

[Note: This exercise helps you deduce algebraically properties of

images that one obtains from explicit ray diagrams.]

Q. A candle flame 1.6 cm high is imaged in a ball bearing of diameter 0.4 cm. If the ball bearing is 20 cm away from the flame, find the location and the height of the image. (Assume the paraxial approximation to hold)

1. 1 mm behind the mirror and 0.08 mm high
2. 1 mm in front of the mirror and 0.08 mm high
3. 1 mm behind the mirror and 0.8 mm high
4. 10 mm in front of the mirror and 0.08 mm high

Q. A person looks into a spherical mirror. The size of the image of his face is twice the actual size of his face. If the face is at a distance of $20\text{cm}$ from the mirror, then the nature and radius of curvature of the mirror is

1. Concave, $80\text{cm}$
2. Concave, $40\text{cm}$
3. Convex, $80\text{cm}$
4. Convex, $40\text{cm}$

Q. 20: An object is placed at 21 cm in front of a concave mirror of radius of curvature 20 cm. A glassslab of thickness 3 cm and refractive index 1.5 is placed close to the mirror in the space betweenthe object and the mirror. Find the position of the final image.

Q. A short linear object of length l lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is approximately equal to [IIT-JEE 1988; BHU 2003; CPMT 2004

1. 
2. 
3. 
4. 

Q. A point object on the principal axis at adistance 15 cm in front of a concave mirror of radius ofcurvature 20 cm has velocity 2 mm/s perpendicular tothe principal axis. The velocity of image at that instantwill be : a.2 mm/sec perpendicular to axis b.4 mm/sec perpendicular to axis c. 0 perpendicular to axis d.8 mm parallel to axis

Q. 88.What is the length of the image of the rod in the mirror, according to the observer in the air?

Q. The image of real object in a convexmirror is 4 cm from the mirror. If the radius of curvature of convex mirror is 24cm, the position of object is

1. 6 cm
2. 4 cm
3. 2 cm
4. 8 cm

Q. At an intersection of hospital hallways, a convex mirror is mounted high on a wall to help people avoid collisions. The mirror has a radius of curvature of 0.550 m. Where will the image of a patient 10.0 m from the mirror be located? (Assume that the patient is along the principal axis of the mirror, and that the paraxial approximation holds.)

1. 26.7 cm, on the side of the object
2. 43.6 cm, on the side of the object
3. 26.7 cm, behind the mirror.
4. 43.6 cm , behind the mirror

Q. A concave mirror having a radius of curvature 40 cm is placed in front of an illuminated point source at a distance 30 cm from it. Find the location of the image.

1. 40 cm , behind the mirror
2. 60 cm, on the side of the object
3. 40 cm, on the side of the object
4. 60 cm, behind the mirror.

Q. With a concave mirror, an object is placed at a distance $x_1$ from the principal focus, on the principal axis. The image is formed at a distance $x_2$ from the principal focus. The focal length of the mirror is

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

Q. A container is filled with water (μ=1.33) up to a height of 332.5 mm. A concave mirror is placed 0.15 m above the water level. The image of an object kept at the bottom of the container is formed 25 CM below the water level. Find the focal length of the concave mirror

Q.

A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

Q. A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror. (The man does not see his face flipped upside down.)

1. 36.8 cm
   
2. 87.5 cm
   
3. 99.4 cm
   
4. 75.6 cm
   

Q. A thief is running away in a car with velocity of 20m/s.A police jeep is following him , which is sighted by thief in his rear view mirror , which is a conves mirror of focal lenght 10m .He observes that the image of jeep is moving towards him with a elocity of 1cm/s.If the magnification of mirror for jeep at that time is 1/10.Find 1) the actual speed of jeep. 2) rate at which magnification is changing Assume the police jeep is on the axis of the mirror

Q. 21.A concave mirror of focal length 8 cm is placed on a table with its reflecting surface turned upwards . The mirror contains a little amount of water in it. At what distance from the pole of the mirror should a point object be placed on the axis of the mirror so that the image and object coincide? Refractive index of water is 4/3.

Q. Find the distance and nature of the image formed by the concave mirror as shown in the figure.

1. $-\frac{40}{3}\text{cm}$, Virtual image
2. $-\frac{40}{3}\text{cm}$, Real image
3. $+\frac{40}{3}\text{cm}$, Virtual image
4. $+\frac{40}{3}\text{cm}$, Real image

Q.

A Cassegrain telescope uses two mirrors as shown in Fig. 9.33. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

Q. A small candle, 2.5cm in size is placed at 27 cm In front of concave mirror of radius of curvature 36cm.at what distance from the mirror should screen be placed in order to obtain sharp image ? Describe the nature and size of the image. If candle has move closer to the mirror, how would the screen have to be moved?

Q. 26.To obtain magnified, inverted image in a concave mirror, object should be held (A) at pole (B) at focus (C)beyond 2F (D)between F and 2F