Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.
In acoustics, reflection causes echoes and is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types of electromagnetic wave, besides visible light. Reflection of VHF and higher frequencies is important for radio transmission and for radar. Even hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors.
Reflection of Light
In acoustics, reflection causes echoes and is used in sonar. In geology, it is important in the study of seismic waves. Reflection is observed with surface waves in bodies of water. Reflection is observed with many types of electromagnetic wave, besides visible light. Reflection of VHF and higher frequencies is important for radio transmission and for radar. Even hard X-rays and gamma rays can be reflected at shallow angles with special "grazing" mirrors.
Reflection of Light
Reflection of light is either specular (mirror-like) or diffuse (retaining the energy, but losing the image) depending on the nature of the interface. Furthermore, if the interface is between a dielectric and a conductor, the phase of the reflected wave is retained, otherwise if the interface is between two dielectrics, the phase may be retained or inverted, depending on the indices of refraction.
A mirror provides the most common model for specular light reflection, and typically consists of a glass sheet with a metallic coating where the reflection actually occurs. Reflection is enhanced in metals by suppression of wave propagation beyond their skin depths. Reflection also occurs at the surface of transparent media, such as water or glass.
Laws of Reflection
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces.
Spherical Mirrors
The reflecting surface of a spherical mirror may be curved inwards or
outwards. A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror.
The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror.The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R.Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole.
A number of rays parallel to the principal axis are falling on a concave mirror.They are all meeting/intersecting at a point on the principal axis of the mirror. This point is called
the principal focus of the concave mirror. For the convex mirror the reflected rays appear to
come from a point on the principal axis. This point is called the principal focus of the convex mirror. The principal focus is represented by the letter F. The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.
Representation of Images Formed by Spherical Mirrors Using Ray Diagrams
(i) A ray parallel to the principal axis, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.
(ii) A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reflection, will emerge parallel to the principal axis.
(iii) A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path.The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.
(iv) A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.
In all the above cases the laws of reflection are followed. At the point of incidence, the incident ray is reflected in such a way that the angle of reflection equals the angle of incidence.
Sign Convention for Reflection by Spherical Mirrors
(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.
(iv) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.
The Mirror Formula
In a spherical mirror, the distance of the object from its pole is called the object distance (u). The distance of the image from the pole of the mirror is called the image distance (v). The distance of the principal focus from the pole is called the focal length (f). The relationship between these three quantities is given by the mirror formula which is
expressed as
(1/v) + (1/u) = (1/f)
This formula is valid in all situations for all spherical mirrors for all positions of the object. One must use the New Cartesian Sign Convention while substituting numerical values for u, v, f, and R in the mirror formula for solving problems.
Magnification
Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image to the height of the object. It is usually represented by the letter m. If h is the height of the object and h′ is the height of the image, then the magnification m produced by a spherical mirror is given by
m = [Height of the image(h')] / [Height of the object(h)]
m = h′ / h
The magnification m is also related to the object distance (u) and image distance (v). It can be expressed as:
Magnification (m) = h' / h = (-v) / u
You may note that the height of the object is taken to be positive as the object is usually placed above the principal axis. The height of the image should be taken as positive for virtual images. However, it is to be taken as negative for real images. A negative sign in the value of the magnification indicates that the image is real. A positive sign in the value of the magnification indicates that the image is virtual.
Thus, this is the end.
Thank you
Laws of Reflection
(i) The angle of incidence is equal to the angle of reflection, and
(ii) The incident ray, the normal to the mirror at the point of incidence
and the reflected ray, all lie in the same plane.
These laws of reflection are applicable to all types of reflecting surfaces
including spherical surfaces.
Spherical Mirrors
The reflecting surface of a spherical mirror may be curved inwards or
outwards. A spherical mirror, whose reflecting surface is curved inwards,
that is, faces towards the centre of the sphere, is called a concave mirror.
A spherical mirror whose reflecting surface is curved outwards, is called
a convex mirror.
The reflecting surface of a spherical mirror forms a part of a sphere.
This sphere has a centre. This point is called the centre of curvature of
the spherical mirror.The radius of the sphere of which the
reflecting surface of a spherical mirror forms a part, is called the radius
of curvature of the mirror. It is represented by the letter R.Imagine a straight
line passing through the pole and the centre of curvature of a spherical
mirror. This line is called the principal axis. Remember that principal
axis is normal to the mirror at its pole.
 |
| Concave Mirror |
 |
| Concave Mirror |
 |
| Convex Mirror |
 |
| Convex Mirror |
A number of rays parallel to the principal axis are falling on a concave mirror.They are all meeting/intersecting at a point on the principal axis of the mirror. This point is called
the principal focus of the concave mirror. For the convex mirror the reflected rays appear to
come from a point on the principal axis. This point is called the principal focus of the convex mirror. The principal focus is represented by the letter F. The distance between the pole and the principal focus of a spherical mirror is called the focal length. It is represented by the letter f.
Representation of Images Formed by Spherical Mirrors Using Ray Diagrams
(i) A ray parallel to the principal axis, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror.
(ii) A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reflection, will emerge parallel to the principal axis.
(iii) A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path.The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.
(iv) A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror or a convex mirror, is reflected obliquely. The incident and reflected rays follow the laws of reflection at the point of incidence (point P), making equal angles with the principal axis.
In all the above cases the laws of reflection are followed. At the point of incidence, the incident ray is reflected in such a way that the angle of reflection equals the angle of incidence.
Sign Convention for Reflection by Spherical Mirrors
(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.
(ii) All distances parallel to the principal axis are measured from the pole of the mirror.
(iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.
(iv) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.
(v) Distances measured perpendicular to and below the principal axis (along –y-axis) are taken as negative.
The Mirror Formula
In a spherical mirror, the distance of the object from its pole is called the object distance (u). The distance of the image from the pole of the mirror is called the image distance (v). The distance of the principal focus from the pole is called the focal length (f). The relationship between these three quantities is given by the mirror formula which is
expressed as
(1/v) + (1/u) = (1/f)
This formula is valid in all situations for all spherical mirrors for all positions of the object. One must use the New Cartesian Sign Convention while substituting numerical values for u, v, f, and R in the mirror formula for solving problems.
Magnification
Magnification produced by a spherical mirror gives the relative extent to which the image of an object is magnified with respect to the object size. It is expressed as the ratio of the height of the image to the height of the object. It is usually represented by the letter m. If h is the height of the object and h′ is the height of the image, then the magnification m produced by a spherical mirror is given by
m = [Height of the image(h')] / [Height of the object(h)]
m = h′ / h
The magnification m is also related to the object distance (u) and image distance (v). It can be expressed as:
Magnification (m) = h' / h = (-v) / u
You may note that the height of the object is taken to be positive as the object is usually placed above the principal axis. The height of the image should be taken as positive for virtual images. However, it is to be taken as negative for real images. A negative sign in the value of the magnification indicates that the image is real. A positive sign in the value of the magnification indicates that the image is virtual.
Thus, this is the end.
Thank you
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