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REFLECTION

Reflection is defined as the bouncing back of a ray of light into the same medium, when it strikes a surface. It occurs on almost all surfaces - some reflect a major fraction of the incident light. Others reflect only a part of it, while absorb the rest.

Reflection of light from surfaces is governed by the two Laws of Reflection:

1. The incident ray, reflected ray and normal at the point of incidence lie on the same plane.
2. The angle which the incident ray makes with the normal (angle of incidence) is equal to the angle which the reflected ray makes with the normal (angle of reflection).

The phenomenon of reflection can be explained with the help of Huygens' construction:

Let us assume a parallel beam of light incident on the surface of a plane mirror (refer to diagram). The wavefronts of the light rays of this incident beam are perpendicular to the direction of incidence.

The wavefront AB of one of the light rays reaches a point A of the reflecting surface at time=0. According to Huygens' principle, this point A now becomes the source of secondary wavelets and emits one which, at time=t, is a hemisphere of radius=ct, where c is the velocity of light. This new wavelet has another wavefront which is perpendicular to the its direction of propagation. Let C be the point where the wavefront of the incident ray reaches after time=t. A tangent is drawn from this point to the hemispherical surface of the wavelet emitted by A. Let this tangent be CD.

Another point P, between A and C is now considered, such that AP/AC = x. Two perpendiculars, PQ and PR are drawn from P onto AB and DC respectively.

Hence,
PR/AD = PC/AC = ((AC - AP)/AC) = (AC(1 - x))/AC = 1-x
Therefore,
Since QP/BC = AP/AC = x
QP = xBC = xct
Therefore the time taken by the wavefront of the incident beam to reach the point P is t1, where
t1 = QP/c = xct/c = xt
As from Huygens principle, this point P emits another secondary wavelet at time t1, whose radius r at time t is given by
r = c ( t - t1 ) = c ( t - xt) = ct (1 - x)

Now, PR is the radius of the secondary wavelet emitted by P at time t, whose wavefront is the same as that of the one emitted by A at time=0, i.e. CD.

But AC is common to both triangles, and also
angle ADC = angle ABC = 90°
Hence, the triangles are congruent. Therefore,
angle BAC = angle DCA.

But the angle between the incident ray and the normal, which is the angle of incidence, is equal to angle BAC. Also, the angle between the reflected ray and the normal, which is the angle of reflection is equal to angle DCA. Hence,
angle of incidence = angle of reflection
It is also clear from geometry that the incident ray, reflected ray and the normal at the point of incidence lie on the same plane. Hence, the two laws of reflection are also proved.

The most common reflecting surfaces today are the mirrors. They can be plane, spherical or a combination of both. Their most popular use is as a looking glass, for which, water was used in the ancient times.

Reflection on the surface of a plane mirror:

When light rays coming from an object reach the eye after reflection from a mirror, the human brain perceives them coming from behind the mirror, and hence the image is formed behind the mirror. It is virtual, laterally inverted, of the same size as the object, and at the same distance behind the mirror as the object is in front.

A virtual image is one in which the light rays do not actually meet, but appear to meet, if produced in a particular direction. It cannot be taken on a screen. The other type of image is a real image, in which light rays actually meet to form the image. It can be taken on a screen. Image formed by a plane mirror is laterally inverted. It means that the right of the object will the left of the image. For e.g., if we stand in front of a mirror wearing a rose on the right side of our shirt, our image will be wearing it on its left side. This phenomenon is known as Lateral Inversion.

Reflection in Spherical Mirrors

So as to apply the laws of reflection to a spherical mirror, a tangent is drawn to its surface at the point of incidence, and is considered to be the surface of a plane mirror at which the ray is incident.

The position, size and nature of the image formed from a convex lens depends on the position of the object in front of the mirror. There are six different positions for an object in front of a concave mirror, in each of which, the nature of image is different.

 Position 1 Object is at infinity The image is formed at the focal point, is real and highly diminished. Position 2 Object is beyond centre of curvature The image is formed between the focal point and centre of curvature, is real, diminished and inverted. Position 3 Object is at the centre of curvature The image is formed at the centre of curvature, is real, of the same size as the object and inverted. Position 4 Object is between centre of curvature and focal point The image is formed beyond the centre of curvature, is real, magnified and inverted. Position 5 Object is at focal point The image is formed at infinity, is real, highly magnified and inverted. Position 6 Object is between focal point and the pole The image is formed on the other side of the mirror, is virtual, magnified and erect.

But for all positions of an object before a convex mirror, the image formed is on the other side of the mirror, virtual, diminished and erect.

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