REFLECTION OF LIGHTS AT CURVED SURFACES

[Audio] REFLECTION OF LIGHTS AT CURVED SURFACES In class 7 and 8 you have learnt about the image formation in plane mirrors. You also discussed about the spherical mirrors. You know that why the curved surfaces are known as spherical mirrors. You might have got many doubts while observing your image in bulged surfaces. Is the image formed by a bulged surface same as the image formed by a plane mirror? Is the mirror used in automobiles a plane mirror? Why is it showing small images? Why does our image appear thin or bulged out in some mirrors? Can we see inverted image in any mirror? Can we focus sun light at a point using a mirror instead of magnifying glass? Are the angle of reflection and angle of incidence also equal for reflection by curved surfaces? Let us discuss about the reflection of light by spherical mirrors in this lesson to get clarity for the above questions..

[Audio] 1.1 Reflection of light by spherical mirrors The first law of reflection tells us A light ray incident at an angle with the normal at the point of incidence will get reflected making equal angle with the normal. This law is true for all surfaces, be it a plane surface or a curved one .The important words here are ‘the angle made with normal at the point of incidence’. If for any surface one can decide the normal and find the incident angle, it is possible to deduce the angle made by the reflected ray. It is very easy to find a normal at any point on the plane surface but for a curved or uneven surface it is not straight forward. Activity 1 Finding the normal to a curved surface fig-1(a) fig-1(b) fig-1(c) Take a small piece of thin foam or rubber (like the sole of a slipper). Put some pins along a straight line on the foam as shown in the fig-1(a). All these pins are perpendicular to the plane of foam. If the foam is considered as a mirror, each pin would represent the normal at that point. Any ray incident at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin-normal. Now bend the foam piece inwards as shown in fig-1(b), what differences will you observe to the pins? They still represent the normal at various points, but you will notice that all the pins tend to converge at a point (or intersect at a point). If we bend the foam piece outwards, we will see that the pins seem to move away from each other or in other words they diverge as shown in fig-1(c). 1.1 Reflection of light by spherical mirrors The first law of reflection tells us A light ray incident at an angle with the normal at the point of incidence will get reflected making equal angle with the normal. This law is true for all surfaces, be it a plane surface or a curved one. The important words here are 'the angle made with normal at the point of incidence'. If for any surface one can decide the normal and find the incident angle, it is possible to deduce the angle made by the reflected ray. It is very easy to find a normal at any point on the plane surface but for a curved or uneven surface it is not straight forward. Activity 1 Finding the normal to a curved surface fig-1(a) fig-1(b) fig-1(c) Take a small piece of thin foam or rubber (like the sole of a slipper). Put some pins along a straight line on the foam as shown in the fig-1(a). All these pins are perpendicular to the plane of foam. If the foam is considered as a mirror, each pin would represent the normal at that point. Any ray incident at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin- normal. Now bend the foam piece inwards as shown in fig-1(b), what differences will you observe to the pins? They still represent the normal at various points, but you will notice that all the pins tend to converge at a point (or intersect at a point). If we bend the.

[Audio] This gives us an idea of what is likely to happen with a spherical mirror. A concave mirror will be like the rubber sole bent inwards (fig-1(b)) and the convex mirror will be like the rubber sole bent out wards (fig-1(c)). For a concave mirror, like these pins in fig-1(b), all normals will converge towards a point. This point is called centre of curvature (C) of the mirror. Recall a little bit of geometry: while learning about circles and tangents, you have learnt that a radius is always perpendicular to the tangent to the circle drawn at the point. This gives us a clue about how we can find normal at a point on a spherical mirror. All that we have to do is to draw a line from the point on the mirror to centre of the sphere. It is much easier to imagine this in a two dimensional fig. as shown in fig-2(a). The concave mirror is actually a part of a big sphere. In order to find this centre point (centre of curvature) we have to think of the centre of the sphere to which the concave mirror belongs. The line drawn from C to any point on the mirror gives the normal at that point. For the ray R, the incident angle is the angle it makes with the normal shown as i and the reflected angle is shown as r in fig-2(b). We know by first law of reflection i = r. The mid point (Geometrical centre) of the mirror is called pole (P) of the mirror. The horizontal line shown in the figs. which passes through the centre of curvature and pole is called principal axis of the mirror. The distance from P to C is radius of curvature (R) of the mirror. Try to construct different reflected rays for any array of rays that are parallel to the principal axis as shown in fig-2(b). What is your observation? This gives us an idea of what is likely to happen with a spherical mirror. A concave mirror will be like the rubber sole bent inwards (fig-1(b)) and the convex mirror will be like the rubber sole bent out wards (fig-1(c)). For a concave mirror, like these pins in fig-1(b), all normals will converge towards a point. This point is called centre of curvature (C) of the mirror. Recall a little bit of geometry: while learning about circles and tangents, you have learnt that a radius is always perpendicular to the tangent to the circle drawn at the point. This gives us a clue about how we can find normal at a point on a spherical mirror. All that we have to do is to draw a line from the point on the mirror to centre of the sphere. It is much easier to imagine this in a two dimensional fig. as shown in fig-2(a). The concave mirror is actually a part of a big sphere. In order to find this centre point (centre of curvature) we have to think of the centre of the sphere to which the concave mirror belongs. The line drawn from C to any point on the mirror gives the normal at that point. For the ray R, the incident angle is the angle it makes with the normal shown as i and the reflected angle.