Rays of light can also be reflected on Curved Surfaces. Curved mirrors are part of a sphere. Parabolic mirrors curved more than the curved mirrors.
There are two types of curved mirrors. They are concave and convex mirrors. In a concave mirror, rays of light converge at the centre but in a convex mirror, rays of light deviate from the centre. Hence, Concave mirror is also called Converging mirror while Convex mirror is also called Diverging mirror.
Uses of Curved mirrors
- Concave mirrors are used as dentist mirrors and shaving mirrors
- Concave mirrors are used as a reflecting telescope
- Convex mirrors are used as driving mirrors because it forms an erect image and give a wide field of view.
Diagram of a concave and convex mirror
Terms used in Curved mirrors
- Pole: This is the centre of the mirror
- Centre of Curvature(c): This is the centre at which the mirror forms a part.
- Radius of curvature (r): This is the distance between the pole and the centre of Curvature.
- Principal Axis: This is an imaginary line that joins the pole to the centre of Curvature.
- Principal Focus(P): It is define as the point at which rays of light that are parallel to the principal Axis converge for a concave mirror and diverge for a convex mirror after reflection.
- Focal length (F): This is define as the distance between the pole and the principal Focus. Mathematically, it is half of the radius of curvature.i.e F = r/2
The diagram below shows parts of a Curved mirror.
Sign Convection in mirror
All these will guide you when solving questions on mirrors.
Convex mirror, F= -ve
Concave mirror, F= +ve
Real image, m&v= +ve
Virtual Image, m&v= -ve
Upright/Erect, m&v= -ve
Inverted, m&v= +ve
Convex mirror, m&v= -ve
Distance between object and image
When the image is real = v-u
When the image is virtual = v+u
Mirror Formula
Where F is focal length, U is object distance, V is image distance, m is magnification.
Let's us take some examples to understand better.
- The driving mirror of a car has a radius of curvature of 1m. A vehicle behind the car is 4m from the mirror. Find the image distance behind the mirror.
Solution
- An object is placed 12cm from a concave mirror of radius 32cm. The image formed is (a) virtual & 48cm behind the mirror (b) real and 48cm in front of the mirror (c) virtual and 19.2cm behind the mirror (d) real and 19.2cm in front of the mirror.
Solution
- An object is placed 20cm from a concave mirror of focal length 10cm. The linear magnification of the image produced is
Solution
- A concave mirror position at a distance of 5cm from an object gives a Magnification of 4. If the image is upright. Calculate the radius of curvature of the mirror.
Solution
- A shaving mirror having a radius of curvature 24cm produces a real image four times the size of the object. The distance of the object from the mirror is
Solution
- A convex mirror produces an image which is 1/4 the size of the an object placed in front of it. If the focal length of the mirror is 16cm. Calculate the distance between the object and its image.
Solution
- An object is located at a distance of 20cm from a concave mirror of radius of curvature 30cm. The separation between the object and the image is ?
Solution
