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Physics Theory : Curved Mirrors

 
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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.

 

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).

 

A convex mirror is a curved mirror with the reflecting surface on the outer side (created by depositing silver metal on the hollow side).

 

curved mirror

The pole (denoted by P in the figure) is defined as the geometric center of the curved mirror.

 

The center of curvature (denoted by C in the figure) of a curved mirror is defined as the center of the hollow glass sphere of which the curved mirror was (previously) a part.

 

The radius of curvature (denoted by CP in the figure) 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 (90o) and equals the radius of curvature.

 

The principal axis of a curved mirror is defined as the imaginary line passing through its pole P and center of curvature C.

 

The principal focus (denoted by F in the figure) 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

 

For constructing ray diagrams, the following rules are worth noting :
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.

 

When the object is at infinity in the case of a concave mirror,
the image formed has the following characteristic 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.

 

When the object is between infinity and the center of curvature in front of a concave mirror,
the image formed has the following characteristic 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.

 

When the object is placed at the center of curvature in front of a concave mirror,
the image formed has the following characteristic 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.

 

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 characteristic 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.

 

When the object is placed at the principal focus in front of a concave mirror,
the image formed has the following characteristic 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.

 

When the object is placed between the pole and the principal focus in front of a concave mirror,
the image formed has the following characteristic 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.

 

When the object is at infinity in the case of a convex mirror,
the image formed has the following characteristic properties.
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.

 

ray diagram for convex mirror

When the object is anywhere between the pole and infinity in front of a convex mirror,
the image formed has the following characteristic properties.
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.

 

Real images are always inverted and can be taken on a screen.
Concave mirrors generally produce real and inverted images (except when the object is between the pole and the principal focus).

 

Virtual images are always erect and cannot be taken on a screen.
Convex mirrors always produce virtual, erect and diminished images.

 

Concave mirrors act as converging mirrors.
Concave mirrors are used as shaving mirrors, as reflectors in flashlights and automobile headlights, and by doctors (e.g., dentists).

 

Convex mirrors act as diverging mirrors.
Convex mirrors are used as rear view mirrors by drivers in vehicles and as reflectors in street lights.

 

Physics Quiz on Curved Mirrors.
 
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