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Image Formation by Spherical Mirrors
Project : OSCAR
Developer : Dhanya.P
Contents
1. Terminologies associated with Spherical/curved mirrors.
2. Rules of reflection for curved mirrors.
3. Mirror Equations
4. Characteristics of the image formed by a concave mirror according to the position of the object .
5. Characteristics of the image formed by a convex mirror according to the position of the object. 6. Interactive Session.
Various terms Associated with Spherical Mirrors
Spherical Mirror :A curved mirror formed by a part of a hollow glass sphere with a reflecting surface (created by depositing silver metal) is also referred to as a spherical mirror.
Concave Mirror:A concave mirror is a curved mirror with the reflecting surface on the hollow side (created by depositing silver metal on the outer curved side).
Convex Mirror : A convex mirror is a curved mirror with the reflecting surface on the outerside
Centre of Curvature : The centre of curvature of a curved mirror is defined as the center of the hollow glass sphere of which the curved mirror was (previously) a part.
Radius of curvature The radius of curvature of a curved mirror is defined as the radius of the hollow glass sphere of which the spherical mirror was (previously) a part. Note that any line drawn from the center of curvature C to the mirror surface meets it at right angle and equals the radius of curvature. Principal Axis :The principal axis of a curved mirror is defined as the imaginary line passing through its pole P and center of curvature C.
Focus :The principal focus is defined as the point on the principal axis where the light rays traveling parallel to the principal axis after reflection actually meet (for a concave mirror) or appear to meet (for a convex mirror).
The principal focus is in front of the concave mirror and is behind the convex mirror.
The focal length (denoted by FP in the figure) is the distance between the pole P and the principal focus F of a curved mirror.Note that the focal length is half the radius of curvature.
Focal Length = Radius of Curvature/2
Pole : The pole is defined as the geometric center of the curved mirror.
Rules of Reflection for Curved Mirrors 1. Any light ray traveling parallel to the principal axis is
reflected by the curved mirror through the principal focus. It either actually passes (for a concave mirror) or appears to pass (for a convex mirror) through the principal focus.
2. Any light ray that passes (for a concave mirror) or appears to pass (for a convex mirror) through the principal focus is reflected by the curved mirror parallel to the principal axis.
3. Any light ray that passes (for a concave mirror) or appears to pass (for a convex mirror) through the center of curvature retraces its initial path after reflection by the curved mirror. This is shown in Slide 7
| | Centre of curvature Focus Pole
1/f = i/do + 1/di Magnification (M) = di/do f – Focal length of the mirror di Distance of the image from the Pole
Mirror Equations
*f is +ve in the case of concave mirror. *f is ve in the case of a convex mirror. * di is +ve if the image is a real image and located on the object's side of the mirror. * di is ve if the image is a virtual image and located behind the mirror.
Characteristics of the Image Formed by a Concave Mirror According to the Position of the Object
When the object is at infinity in the case of a concave mirror, the image formed has the following properties. 1. The image is real. 2. The image is inverted. 3. The image is highly diminished to a point. 4. The image is formed at the principal focus in front of the concave mirror.
image
P
Object at Infinity
FC
When the object is between infinity and the center of curvature in front of a concave mirror, the image formed has the following properties.
1. The image is real. 2. The image is inverted. 3. The image is diminished. 4. The image is formed between the principal focus and the center of curvature in front of the concave mirror.
This is shown below
|| C F
object
image
P
Object beyond the Centre of Curvature
When the object is placed at the principal focus in front of a concave mirror, the image formed has the following properties.
1. The image is real. 2. The image is inverted. 3. The image is highly enlarged. 4. The image is formed at infinity in front of the concave mirror.
|| C
F
object
P
Object at the Principal Focus
When the object is placed between the pole and the principal focus in front of a concave mirror,the image formed has the following properties.
1. The image is virtual. 2. The image is erect. 3. The image is enlarged. 4. The image is formed behind the concave mirror.
||
FC P
Object between Pole and Principal Focus
Object
Image
When the object is placed between the principal focus and the center of curvature in front of a concave mirror,the image formed has the following properties.
1. The image is real. 2. The image is inverted. 3. The image is enlarged. 4. The image is formed beyond the center of curvature in front of the concave mirror, but not at infinity.
|| F
C
Object is between Centre of Curvature and Focus
P
Object
Image
When the object is placed at the center of curvature in front of a concave mirror,the image formed has the following properties.
1. The image is real. 2. The image is inverted. 3. The image is of the same size as the object. 4. The image is formed at the center of curvature in front of the concave mirror.
| |C FP
Object is at the Centre of Curvature
Object
Image
Image Formation by a Convex Mirror
Characteristics of the Image Formed according to the position of the object
When the object is at Infinity 1. The image is virtual. 2. The image is erect 3. The image is highly diminished to a point 4. The image is formed at the principal focus behind the convex mirror.
When the object is anywhere between the pole and infinity in front of the convex mirror
1. The image is virtual. 2. The image is erect. 3. The image is diminished. 4. The image is formed between the principal focus and the pole behind the convex mirror.
| |Object Image F C
When the object is anywhere between the pole and infinity in front of the convex mirror
Interactive Session There will be a window having two buttons named ' Concave Mirror' and 'Convex Mirror' . User can click any of them.While clicking on the 'Concave Mirror' button, a concave mirror, object and its image will be displayed in the window. (This is shown in slide 25) User can change the position of the object along the principal axis of the concave mirror by clicking the bottom of the object and dragging the mouse along the principal axis. and can see how the image is formed accordingly. The conditions that he can distinguish in the case of a concave mirror are 1. Object at infinity 2. Object between infinity and C 3. Object at C 4. Object between C and F 5. Object at F 6. Object between F and P
If the user clicks on the 'Convex Mirror' button,then a convex mirror, and object and its image will be shown.
User can change the position of the object in front of the mirror along the principal axis by dragging the mouse horizontally.
Concave Mirror Convex Mirror
|| F
C
P
(Clicked)
Object
Image
THE END