Reflection of light from Spherical Mirrors
Spherical Mirror
What is a spherical mirror?
The cut part of a hollow glass sphere is called a spherical surface, if one side of the spherical surface is polished with silver or nickel, then it is called a spherical mirror.
Important Terms about Spherical Mirror :
Pole of Mirror
The midpoint of the mirror is called pole, it is represented by O.
Center of Curvature
The center of the sphere from which the spherical mirror is made is called the center of curvature, it is represented by C.
Radius of Curvature
The radius of the sphere from which the spherical mirror is made is called the radius of curvature, it is represented by R. `OC = R`
Principal Focus
The light ray coming parallel to the principal axis after reflection from the spherical mirror passes through the point on the principal axis is called the focus point of the spherical mirror, it is represented by F.
Focal Length
The distance between the pole (O) and the focus point of a spherical mirror (F) is called the focal length, it is represented by f. `OF = f`
Principal Axis of Mirror
The imaginary line on which the pole (O ), the focus point (F), and the center of curvature (C) of the spherical mirror are present is called the principal axis.
Aperture of Spherical Mirror
The width of the open part of the spherical mirror is called the aperture, it is the entire reflecting surface.
Sign Convention for Spherical Mirrors
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| Sign Convention |
(1) If the distance is to be measured in the direction of the incident ray, then the sign is taken as positive.
(2) If the measurement is to be taken in the opposite direction of the incident ray, then the sign is taken as negative.
(3) The positive sign is used when moving upwards from the X-axis.
(4) A negative sign is used when moving down from X-axis.
(5) All distances are measured from the pole.
Laws of Reflection
(i) Measure all distances from the pole (point O) of the mirror.
(ii) A ray of light incident parallel to the principal axis passes through the focus point after reflection from the spherical mirror.
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Laws of Reflection from a Spherical Mirror
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(iii) The light ray coming from the focus point becomes parallel to the principal axis after reflection from the spherical mirror.
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| Laws of Reflection from a Spherical Mirror |
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(iv) Light ray pass through the center of curvature after reflection from the mirror passes back through the center of curvature.
(or)
If the light ray comes from the center of curvature then after reflection it passes through the center of curvature again.
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Laws of Reflection from a Spherical Mirror
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(v) The angle with which a ray of light is incident at the pole is reflected back from the same angle.
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Laws of Reflection from a Spherical Mirror
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Image Formation by Spherical Mirror
Creating a reflection
Two rays of light pass through the object whose image is to be obtained. The image of the object is obtained at the point where these light rays meet after reflection from the spherical mirror.
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Image Formation by Spherical Mirror
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If the rays of light meet on their own, the image is real.
If the light rays are meet backward side, then the virtual image is obtained.
Uses of Concave Mirror
(i) As reflectors in torches, vehicle headlights, and searchlights to get powerful beams of light.
(ii) Reflecting telescopes. These instruments are used to image those distant objects. So, a concave is called a converging mirror.
(iii) As shaving mirrors. It is used for personal benefit, like magnifying the image of the face for shaving or applying makeup
(iv) They are used by dentists to see large images of teeth. They are used in the field of solar energy to focus sun’s rays for heating solar furnaces.
(v) It collects light from large area, then focuses it into a small spot area. as it is in the case of concentrated solar power.
(vi) Concave mirrors are used in a very important optical
cavities, which is important in the construction of the laser.Note :
The concave mirrors have an important advantage over the optics of the lenses optics, that they do not introduce chromatic aberration.
Q. What is a spherical mirror and its types?
If a small part is cut off from a hollow sphere of glass, then it is called a spherical surface and if it is polished with another shiny material like silver or nickel, then a spherical mirror is formed. Reflection takes place in a spherical mirror. Spherical mirrors are of two types, first concave, and second convex.
Q. What are the different types of mirrors in optics?
Plane mirror:
The images formed by a plane mirror are the reflected images in their normal proportions but reversed from left to right.
Two type of Spherical mirrors
What is convex mirror
The spherical mirrors are curved outward and the nature of the image is virtual and erect. Size is diminished for a real object.
What is concave mirror
Spherical mirrors that are curved inward and the image obtained from these mirrors depends on the placement of the object.
Q. What are the four rules for image formation by spherical mirrors?
Rule 1: After reflection, a ray of light parallel to the principal axis appears to be coming from focus.
Rule 2: A ray of light going towards center of curvature is reflected back along the same path.
Rule 3: After reflection, a ray of light going towards the focus becomes parallel to the principal axis.
Rule 4: Ray of light which is incident at the pole is reflected back making the same angle with the principal axis.
MCQ On Spherical Mirrors With Answers
Spherical mirrors Question 1
Where is image formed when an object is placed beyond the Centre of curvature of concave mirror?
( 1 ) At the Centre of Curvature
( 2) Beyond the Centre of Curvature
(3) At Infinity
(4) Between Focus and the Centre of Curvature
Answer (4) Between Focus and the Centre of Curvature
Spherical mirrors Question 2
An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm to towards the mirror, the displacement of the image will be -
( i ) 20 cm away from the mirror
( ii) 36 cm away from the mirror
(iii) 36 cm towards the mirror
(iv) 30 cm towards the mirror
Answer (2) 36 cm away from the mirror
Spherical mirrors Question 3
A car moving with a constant speed of 60 km/h on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km/h. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two car were maintaining their speeds, which of the following statement (s) is/are correct?
( i ) The speed of the car in the rear is 65 km/h
( ii) In the side mirror the car in the rear would appear to approach with a speed of 5 km/h to the driver of the leading car.
(iii) In the rear view mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
(iv) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.
Answer (3) In the rear view mirror the speed of the approaching car would appear to decrease as the distance between the cars decreases.
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