Basic about reflection of light at curved surfaces 10th class
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REFLECTION AT CURVED SURFACES
Introduction
We have already looked at reflection by plane mirrors in topic 8. When the reflecting surface is instead curved, we call it a curved mirror. There are two types of curved mirrors; concave and convex mirror. Curved mirrors whose reflecting surfaces curve inwards are called concave mirrors while those whose reflecting surfaces bulge outwards are called convex mirrors.
Terms
Curved mirrors are parts of a sphere. The following terms are used in curved mirrors:
Pole P- it is the centre of the mirror.Centre of curvature C- it is the centre of the sphere of which the mirror is part.Radius of curvature r- it is the radius of the sphere of which the mirror is part.Principal axis- it is a line drawn through the pole of the mirror and the centre of curvature.Principal focus F – for a concave mirror, it is the point at which all rays parallel and close to the principal axis converge at after reflection. In the case of a convex mirror, it is the point at which all rays parallel and close to the principal axis appear to diverge from after reflection.(See the figure above). It is also called the focal point.Focal plane- it is a plane perpendicular to the principal axis and passes through the focal point. It is the plane where parallel rays but not parallel to the principal axis converge at or appear to diverge from after reflection.Focal length f- it is the distance between the pole of the mirror and its focal point.
When rays are produced behind the mirror, they are indicated using dotted lines. This means that they are imaginary or virtual. Hence the focal point and focal length of a concave mirror are real while the focal point and focal length of a convex mirror arevirtual. A real focal length is given a positive signwhile a negative focal length is given a negative sign.
Ray diagrams
Curved mirrors form images when two rays intersect or appear to intersect. In ray diagrams, we use the following symbols to represent the two curved mirrors:
There are four important rays used in ray diagrams. They include:
A ray passing through C or appearing to pass through C:
The ray is reflected along the same path.
A ray parallel and close to the principal axis.
The ray is reflected through the principal focus F for a concave mirror or appear to come from the principal focus of the convex mirror.
A ray passing through the principal focus F or appearing to pass through F
The reflected ray moves parallel to the principal axis (by the principle of reversibility of light).
A ray incident at the pole of the mirror.
The ray is reflected making the same angle with the principal axis as the incident ray (i.e <i=<r).
Image formation by curved mirrors
The table below provides a summary of how a concave and convex mirror forms images:
Position of the object
Image formation by concave mirror
Image formation by convex mirror
Object at infinity
Image formed is inverted, real , diminished and formed at F.
Image formed is upright, virtual and diminished.
Object beyond C
Image formed is real, inverted and diminished.
Image formed is virtual, upright and diminished.
Object at C
Image formed is real, inverted and same size as the object
Image formed is virtual, upright and diminished.
Object between C and F
Image formed is real, inverted and magnified.
Image formed is virtual, upright and diminished.
Object at F
Image formed is real, inverted and at infinity.
Image formed is virtual, upright and diminished.
Object between F and P
Image formed is virtual, upright and magnified.
Image formed is virtual, upright and diminished.
Note that a concave mirror always forms real and inverted and images except when the object is placed between the focal point and the pole of the mirror when it forms a virtual and inverted image. On the other hand, a convex mirror always forms a virtual, erect and diminished image.
A real image is that image formed by actual intersection of real rays while a virtual image is formed by imaginary rays. Furthermore, a real image can be formed on a screen while a virtual image cannot be formed on a screen.
Introduction
We have already looked at reflection by plane mirrors in topic 8. When the reflecting surface is instead curved, we call it a curved mirror. There are two types of curved mirrors; concave and convex mirror. Curved mirrors whose reflecting surfaces curve inwards are called concave mirrors while those whose reflecting surfaces bulge outwards are called convex mirrors.
Terms
Curved mirrors are parts of a sphere. The following terms are used in curved mirrors:
Pole P- it is the centre of the mirror.Centre of curvature C- it is the centre of the sphere of which the mirror is part.Radius of curvature r- it is the radius of the sphere of which the mirror is part.Principal axis- it is a line drawn through the pole of the mirror and the centre of curvature.Principal focus F – for a concave mirror, it is the point at which all rays parallel and close to the principal axis converge at after reflection. In the case of a convex mirror, it is the point at which all rays parallel and close to the principal axis appear to diverge from after reflection.(See the figure above). It is also called the focal point.Focal plane- it is a plane perpendicular to the principal axis and passes through the focal point. It is the plane where parallel rays but not parallel to the principal axis converge at or appear to diverge from after reflection.Focal length f- it is the distance between the pole of the mirror and its focal point.
When rays are produced behind the mirror, they are indicated using dotted lines. This means that they are imaginary or virtual. Hence the focal point and focal length of a concave mirror are real while the focal point and focal length of a convex mirror arevirtual. A real focal length is given a positive signwhile a negative focal length is given a negative sign.
Ray diagrams
Curved mirrors form images when two rays intersect or appear to intersect. In ray diagrams, we use the following symbols to represent the two curved mirrors:
There are four important rays used in ray diagrams. They include:
A ray passing through C or appearing to pass through C:
The ray is reflected along the same path.
A ray parallel and close to the principal axis.
The ray is reflected through the principal focus F for a concave mirror or appear to come from the principal focus of the convex mirror.
A ray passing through the principal focus F or appearing to pass through F
The reflected ray moves parallel to the principal axis (by the principle of reversibility of light).
A ray incident at the pole of the mirror.
The ray is reflected making the same angle with the principal axis as the incident ray (i.e <i=<r).
Image formation by curved mirrors
The table below provides a summary of how a concave and convex mirror forms images:
Position of the object
Image formation by concave mirror
Image formation by convex mirror
Object at infinity
Image formed is inverted, real , diminished and formed at F.
Image formed is upright, virtual and diminished.
Object beyond C
Image formed is real, inverted and diminished.
Image formed is virtual, upright and diminished.
Object at C
Image formed is real, inverted and same size as the object
Image formed is virtual, upright and diminished.
Object between C and F
Image formed is real, inverted and magnified.
Image formed is virtual, upright and diminished.
Object at F
Image formed is real, inverted and at infinity.
Image formed is virtual, upright and diminished.
Object between F and P
Image formed is virtual, upright and magnified.
Image formed is virtual, upright and diminished.
Note that a concave mirror always forms real and inverted and images except when the object is placed between the focal point and the pole of the mirror when it forms a virtual and inverted image. On the other hand, a convex mirror always forms a virtual, erect and diminished image.
A real image is that image formed by actual intersection of real rays while a virtual image is formed by imaginary rays. Furthermore, a real image can be formed on a screen while a virtual image cannot be formed on a screen.
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