Mathematics Of Curved Mirrors Worksheet Answers
Concave MirrorConvex MirrorImage Formation By Concave MirrorImage Formation By Convex Mirror
What is a Mirror?
A mirror is a reflective surface that bounces off light, producing either a real image or a virtual image. When an object is placed in front of a mirror, the image of the same object is seen in the mirror. The object is the source of the incident rays and the image is formed by the reflected rays. Based on the interaction of light, the images are classified as either a real image or a virtual image. A real image occurs when the light rays actually intersect while virtual images occur due to the apparent divergence of light rays from a point.
Ray diagrams help us trace the path of the light for the person to view a point on the image of an object. Ray diagram uses lines with arrows to represent the incident ray and the reflected ray. It also helps us trace the direction in which the light travels.
Plane Mirror vs Spherical Mirrors
Mirrors are made into different shapes for different purposes.
The two of the most prominent types of mirrors are:
- Plane Mirrors
- Spherical Mirrors
A plane mirror is a flat, smooth reflective surface. A plane mirror always forms a virtual image that is upright, and of the same shape and size as the object, it is reflecting. A spherical mirror is a mirror that has a consistent curve and a constant radius of curvature. The images formed by a spherical mirror can either be real or virtual. Spherical mirrors are of two types as:
-
- Concave Mirror
- Convex Mirror
In the next few sections, let us learn in-depth about the characteristics of convex and concave mirrors and the images formed by them when the object is kept at different positions.
Spherical Mirrors
Spherical mirrors are the mirrors having curved surfaces that are painted on one of the sides. Spherical mirrors in which inward surfaces are painted are known as convex mirrors, while the spherical mirrors in which outward surfaces are painted are known as concave mirrors.
Concave Mirror
If a hollow sphere is cut into parts and the outer surface of the cut part is painted, then it becomes a mirror with its inner surface as the reflecting surface. This type of mirror is known as a concave mirror.
Characteristics of Concave Mirrors
- Light converges at a point when it strikes and reflects back from the reflecting surface of the concave mirror. Hence, it is also known as a converging mirror.
- When the concave mirror is placed very close to the object, a magnified and virtual image is obtained.
- However, if we increase the distance between the object and the mirror then the size of the image reduces and a real image is formed.
- The image formed by the concave mirror can be small or large or can be real or virtual.
Convex Mirror
If the cut part of the hollow sphere is painted from inside, then its outer surface becomes the reflecting surface. This kind of mirror is known as a convex mirror.
Characteristics of Convex Mirrors
- A convex mirror is also known as a diverging mirror as this mirror diverges light when they strike on its reflecting surface.
- Virtual, erect, and diminished images are always formed with convex mirrors, irrespective of the distance between the object and the mirror.
Image Formation by Spherical Mirrors
Guidelines for Rays Falling on the Concave and Convex Mirrors
- When a ray strikes concave or convex mirrors obliquely at its pole, it is reflected obliquely.
- When a ray, parallel to principal axis strikes concave or convex mirrors, the reflected ray passes through the focus on the principal axis.
- When a ray, passing through focus strikes concave or convex mirrors, the reflected ray will pass parallel to the principal axis.
- A ray passing through the center of curvature of the spherical mirror will retrace its path after reflection.
Image Formation By Concave Mirror
By changing the position of the object from the concave mirror, different types of images can be formed. Different types of images are formed when the object is placed:
- At the infinity
- Beyond the center of curvature
- At the center of curvature
- Between the center of curvature and principal focus
- At the principal focus
- Between the principal focus and pole
Recommended Video
Concave Mirror Ray Diagram
- Concave Mirror Ray Diagram lets us understand that, when an object is placed at infinity, a real image is formed at the focus. The size of the image is much smaller compared to that of the object.
- When an object is placed behind the center of curvature, a real image is formed between the center of curvature and focus. The size of the image is smaller than compared to that of the object.
- When an object is placed at the center of curvature and focus, the real image is formed at the center of curvature. The size of the image is the same as compared to that of the object.
- When an object is placed in between the center of curvature and focus, the real image is formed behind the center of curvature. The size of the image is larger than compared to that of the object.
- When an object is placed at the focus, the real image is formed at infinity. The size of the image is much larger than compared to that of the object.
- When an object is placed in between focus and pole, a virtual and erect image is formed. The size of the image is larger than compared to that of the object.
Summary
| S. No | Position of Object | Position of Image | Size of Image | Nature of Image |
| 1 | At infinity | At the focus F | Highly Diminished | Real and Inverted |
| 2 | Beyond the center of curvature C | Between F and C | Diminished | Real and Inverted |
| 3 | At the center of curvature C | At C | Same Size | Real and Inverted |
| 4 | Between C and F | Beyond C | Enlarged | Real and Inverted |
| 5 | At focus F | At Infinity | Highly Enlarged | Real and Inverted |
Image Formation By Convex Mirror
The image formed in a convex mirror is always virtual and erect, whatever be the position of the object. In this section, let us look at the types of images formed by a convex mirror.
- When an object is placed at infinity, a virtual image is formed at the focus. The size of the image is much smaller than compared to that of the object.
- When an object is placed at a finite distance from the mirror, a virtual image is formed between the pole and the focus of the convex mirror. The size of the image is smaller than compared to that of the object.
Summary
| S. No | Position Of Object | Position of Image | Size of Image | Nature of Image |
| 1 | At Infinity | At the focus F, behind the mirror | Highly diminished | Virtual and Erect |
| 2 | Between Infinity and the Pole | Between P and F, behind the mirror | Diminished | Virtual and Erect |
Stay tuned with BYJU'S to know more about concave-convex mirrors, plane mirrors, and much more.
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Frequently Asked Questions
How do convex mirrors work?
A convex mirror is a diverging mirror in which the reflective surface bulges towards the light source. They are not used to focus light as they reflect light outwards. The image formed by convex mirrors are smaller than the object but gets larger as they approach the mirror.
How do concave mirrors work?
A concave mirror has a reflective surface that is curved inward and away from the light source. Concave mirrors reflect light inward to one focal point. Unlike convex mirrors, the image formed by a concave mirror shows different image types depending on the distance between the object and the mirror.
Give examples of concave and convex mirrors.
Torch lights, automobile headlights are examples of concave mirrors. Magnifying glasses, telescopes are examples of convex mirrors.
What is the difference between a concave mirror and a convex mirror?
Spherical mirrors whose inner side is reflecting are called concave mirrors. Spherical mirrors whose outer side is reflecting are called convex mirrors.
Can you distinguish concave and convex mirrors without touching them?
When you keep an object in front of a concave mirror, an enlarged image of the object is formed when it is kept close to the mirror and an inverted image of the object is formed when it is kept at a distance. A convex mirror always forms a small and an erected image of the object.
Mathematics Of Curved Mirrors Worksheet Answers
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