1. Answer the following questions.

1. Explain the difference between a plane mirror, a concave mirror, and a convex mirror with respect to the type and size of the images produced.

 Answer. Plane Mirror:

• Type of Image: Virtual and upright.
• Size of Image: The size of the image formed in a plane mirror is equal to the size of the object.
• Characteristics: Plane mirrors produce virtual images, meaning the rays of light appear to diverge from a point behind the mirror. These images are of the same size as the object and are formed at the same distance behind the mirror as the object is in front of it. They are upright and laterally inverted.
• Concave Mirror:
• Type of Image: Real or virtual, depending on the position of the object.
• Size of Image: The size of the image formed by a concave mirror can vary. If the object is placed beyond the focal point, the image is real, inverted, and diminished in size. If the object is placed between the focal point and the mirror, the image is real, inverted, and enlarged in size.
• Characteristics: Concave mirrors can form both real and virtual images. Real images are formed when the object is placed beyond the focal point, while virtual images are formed when the object is placed between the focal point and the mirror. The image formed can be either magnified or diminished, depending on the position of the object relative to the mirror.

Convex Mirror:

Type of Image: Virtual and upright.

Size of Image: The size of the image formed by a convex mirror is always diminished.

Characteristics: Convex mirrors always produce virtual images that are upright and diminished in size. The image formed appears to be located behind the mirror, and the rays of light diverge upon reflection. These mirrors are commonly used in applications such as rear-view mirrors in vehicles, where a wider field of view is required.

plane mirrors produce virtual images of the same size as the object, concave mirrors can produce both real and virtual images of varying sizes, and convex mirrors produce virtual images that are always diminished in size. These differences arise from the unique reflective properties of each type of mirror.

b. Describe the positions of the source of light with respect to a concave mirror in

1. Torch light

(a) Torch Light: Positioned precisely at the focal point.

2. Projector lamp

(b) Projector Lamp: Located precisely at the centre of curvature.

3. Floodlight

(c) Floodlight: Positioned just beyond the center of curvature.

d. Why are the mirrors fitted on the outside of cars convex?

Answer: Convex mirrors in rear-view mirrors produce upright, virtual, and smaller images, providing drivers with a broad view in a compact mirror.

e. Why does obtaining the image of the sun on a paper with the help of a concave mirror burn the paper?

When sunlight strikes the concave mirror, it converges, focusing on the focal plane.

This convergence amplifies the intensity of the sunlight, leading to the sun’s image burning a piece of paper when reflected through the concave mirror.

f. If a spherical mirror breaks, what type of mirrors are the individual pieces?

Answer:

If a spherical mirror breaks into smaller pieces, its radius of curvature and focal length remain unchanged. Consequently, it will still function as a spherical mirror, maintaining its optical properties.

2. What sign conventions are used for reflection from a spherical mirror?

Answer: As per the Cartesian sign convention, the pole of the mirror serves as the starting point or origin. The principal axis is aligned with the X-axis. Here are the conventions:

• Objects are placed on the left side of the mirror.
• Distances along the principal axis from the mirror’s pole are measured.
• Distances to the right of the pole are positive, and to the left are negative.
• Vertical distances above the principal axis are positive and below are negative.
• Concave mirrors have a negative focal length, while convex mirrors have a positive focal length.

3. Draw ray diagrams for the cases of images obtained in concave mirrors as described in the table

Answer:

• A ray diagram for the object at infinity for a concave mirror.

Object at infinity for concave mirror

Image position	Nature of image
Image position at Focus	The nature of the image is Real, inverted and point image

(b) A ray diagram for object beyond centre of curvature for a concave mirror.

An object beyond the centre of curvature for a concave mirror

Image position	Nature of image
Image position between the center of curvature and focus.	The nature of the image is Real, inverted and diminished

(c) A ray diagram for object at the centre of curvature for a concave mirror.

object at the centre of curvature for a concave mirror.

Image position	Nature of image
Image position at the centre of curvature	The nature of the image is Real, inverted and same size.

(d) A ray diagram for object between F and C for a concave mirror.

Object between F and C for a concave mirror.

Image position	Nature of image
Image position beyond the centre of curvature	The nature of the image is Real, inverted and magnified

(e) A ray diagram for an object at focus for a concave mirror.

Object at a focus for a concave mirror.

Image position	Nature of image
Image position at infinity	The nature of the image is Real, inverted and highly magnified

(f) A ray diagram for object between pole and focus for a concave mirror.

The object between pole and focus for a concave mirror.

4. Which type of mirrors are used in the following?

Periscope, floodlight, shaving mirror, kaleidoscope, street lights, headlamps of a car.

Objects	Type of Mirror
Periscope	Plane Mirror
Floodlights	Concave Mirror
Shaving Mirror	Concave Mirror
kaleidoscope	Plane Mirror
Street lights	Convex Mirror
Headlamps of the car	Concave Mirror

5. Solve the following examples

a. An object of height 7 cm is kept at a distance of 25 cm in front of a concave mirror. The focal length of the mirror is 15 cm. At what distance from the mirror should a screen be kept so as to get a clear image? What will be the size and nature of the image?

Solution. First, let’s understand the situation. We have a concave mirror, an object placed in front of it, and we want to know where to place a screen to see a clear image of the object.

The object is placed at a distance of 25 cm from the concave mirror.

The focal length of the mirror is given as 15 cm. For a concave mirror, the focal length is negative.

Now, let’s find out the position of the image and its size.

Formula: 1/v+1/u=1/f

Where:

f is the focal length of the mirror (given as -15 cm)

 v is the distance of the image from the mirror (which we want to find)

 u is the distance of the object from the mirror (given as -25 cm, negative because the object is in front of the mirror)

So, the distance of the image from the mirror is 37.5 cm.

Now, to find the size and nature of the image, we use the magnification formula:

b. A convex mirror has a focal length of 18 cm. The image of an object kept in front of the mirror is half the height of the object. What is the distance of the object from the mirror?

©A 10 cm long stick is kept in front of a concave mirror having a focal length of 10 cm in such a way that the end of the stick closest to the pole is at a distance of 20 cm. What will be the length of the image?

6. Three mirrors are created from a single sphere. Which of the following:

pole, centre of curvature, radius of curvature, principal axis – will be common to them and which will not be common?

The mirror created  from a single sphere

The center of curvature and the radius of curvature remain consistent across all three fragments, ensuring uniformity in their reflective properties.

However, the pole and principal axis differ individually for each piece, contributing to their unique geometrical characteristic.