LIGHT - REFLECTION Contents: How do we see objects? Common phenomena of light Straight line path of light Particle and wave nature of light Spherical mirrors How to draw ray diagram? Image formation by a concave mirror Image formation by a convex mirror Uses of concave and convex mirror Sign convention for reflection by spherical mirror Mirror formula and magnification formula Plane Mirror Created by C. Mani, Deputy Commissioner, KVS RO Gurgaon

What makes things visible? We are unable to see anything in a dark room. On lighting up the room, things become visible. Eye What makes things visible? An object reflects light that falls on it. The reflected light, when received by our eyes, enables us to see things.

- image formation by mirrors - image formation by lenses Common phenomena of light are - image formation by mirrors - image formation by lenses - twinkling of stars - beautiful colours of a rainbow - bending of light by a medium - sparkling of diamonds - colours formed on thin oil films - colours formed in soap bubbles - reddish appearance of sun while rising and setting - blue colour of the sky and many more

• • A small source of light casts a sharp shadow of an opaque object. X Y X Y S • Shadow S • Opaque Slit Opaque object Shadow Screen Screen This shows that light travels in a straight line path.

Phenomenon like interference of light exhibits wave nature of light. Bright Band Dark Band S1 • Bright Band S2 • Dark Band Bright Band

Phenomenon like diffraction of light also exhibits wave nature of light. Shadow X Y X Y S • Shadow S • Opaque Slit Opaque object Shadow Screen Screen Diffraction at an obstacle Diffraction at a slit X & Y – Region of diffraction

Phenomenon like polarisation of light also exhibits wave nature of light. Optic Axis • Unpolarised light Plane Polarised light Plane Polarised light Polariser Tourmaline Crystal Analyser Tourmaline Crystal • 90° No light Plane Polarised light Unpolarised light

Phenomenon like photo electric effect exhibits particle nature of light. UV Visible light Photoelectrons Photoelectrons Metals Alkali Metals Visible light No photoelectrons Metals other than Alkali Metals

REFLECTION OF LIGHT Laws of Reflection of Light: Normal Incident Ray Reflected Ray Plane containing incident ray, reflected ray and normal i r Plane mirror Laws of Reflection of Light: The angle of incidence is equal to the angle of reflection. The incident ray, the normal to the mirror at the point of incidence and the reflected ray, all lie in the same plane. Note: These laws of reflection are applicable to all types of reflecting surfaces including spherical surfaces.

Formation of image by a plane mirror Normal Normal Object Plane Mirror Image Properties of image formed by a plane mirror Image is always virtual and erect. Size of the image is equal to the size of the object. Image is as far behind the mirror as the object is in front of it. Image is laterally inverted.

SPHERICAL MIRRORS Mirrors whose reflecting surfaces are spherical are called ‘spherical mirrors’. A spherical mirror whose reflecting surface is curved inwards, i.e. faces towards the centre of the mirror, is called a concave mirror. A spherical mirror whose reflecting surface is curved outwards, i.e. faces away from the centre of the mirror, is called a convex mirror. Concave Mirror Convex Mirror Reflecting surface Painted surface

Concave Mirror Convex Mirror M N M N P X C F X P F C f R f R Pole (P) is the centre of reflecting surface lying on the surface. Centre of curvature (C) is the centre of the imaginary sphere from which spherical mirror is cut out. Radius of curvature (R) is the distance between the pole and the centre of curvature. Principal axis (PCX or CPX) is the line passing through the pole and the centre of curvature and extending to ∞. It is the normal to the mirror at the pole. Principal Focus (F) is the point on the principal axis at which the incident rays of light parallel to principal axis either really pass through or appear to pass through after getting reflected from the mirror. Focal length (f) is the distance between the pole and the principal focus.

Rays to be considered for drawing Ray Diagram Radius of curvature is approximately twice the focal length. R ≈ 2f Aperture (MN) is the diameter of the reflecting surface. Note that it is not the diameter of the sphere from which the mirror is cut out. Rays to be considered for drawing Ray Diagram The intersection of at least two reflected rays give the position of image of the point object. Any two of the following rays can be considered for locating the image. 1. 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. r i i r P C F P F C

2. 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. i C P F F C P r i r 3. 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. i.e. retraces the path. F C P F C P

In all the above cases the laws of reflection are followed. 4. A ray incident obliquely to the principal axis, towards the pole is reflected obliquely. C P F F C P i i r r Note: 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.

Image formation by a concave mirror 1) When object is placed at infinity: Parallel rays from ∞ C P F i Position of image: At F Nature of image : Real & inverted iii) Size of image : Very small (Highly Diminished) r I 2) When object (AO) is placed beyond C (2F): A O C F P Position of image: Between C & F Nature of image : Real & inverted iii) Size of image : Smaller than object (Diminished) i r B I

3) When object (CO) is placed at C: F P O Position of image: At C Nature of image : Real & inverted iii) Size of image : Same size as that of the object i r I 4) When object (AO) is placed between C & F: C F P Position of image: Beyond C Nature of image : Real & inverted iii) Size of image : Larger than object (Enlarged) A O B I

5) When object (FO) is placed at F: Position of image: At ∞ Nature of image : Real & inverted iii) Size of image : Very large (Highly enlarged) O Parallel rays meet at ∞ 6) When object (AO) is placed between F & O: B I Position of image: Behind the mirror Nature of image : Virtual & erect iii) Size of image : Larger than the object C F P O A Eye Rays diverge

Image formation by a concave mirror for different positions of the object Position of the object Position of the image Size of the image Nature of the image At infinity At F Highly diminished Real and inverted Beyond C Between F and C Diminished Real and inverted At C Same size Real and inverted Between F and C Beyond C Enlarged Real and inverted At F At infinity Highly enlarged Real and inverted Between P and F Behind the mirror Enlarged Virtual and erect

Image formation by a convex mirror Position of image: Behind the mirror Nature of image : Virtual & erect iii) Size of image : Smaller than the object r A O i C P F I B Image formation by a convex mirror for any position of the object Position of the object Position of the image Size of the image Nature of the image At infinity At F behind the mirror Highly diminished Virtual and erect Between infinity and the pole P Between P and F behind the mirror Diminished

Uses of concave mirror Uses of convex mirror Concave mirrors are used in torches, search-lights and headlights of vehicles. They are used as shaving mirrors. They are used by dentists to see large images of the teeth. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces. Uses of convex mirror Convex mirrors are used as rear view mirrors in vehicles as they form diminished images of the large objects on the road. They are used as magic mirrors and to form funny images.

Sign Conventions for Reflection by Spherical Mirrors (New Cartesian Sign Convention) The object is always placed to the left of the mirror. i.e. the incident rays from the object always move from left to right. All distances parallel to the principal axis are measured from the pole (P) of the mirror. All the distances measured to the right of the Pole (along +ve x-axis) are taken +ve while those measured to the left of the Pole (along - ve x-axis) are taken –ve. Distances measured perpendicular to and above the principal axis (along +ve y-axis) are taken +ve while those measured below the principal axis (along –ve y-axis) are taken –ve. Note: While solving numerical problems, new Cartesian sign convention must be used for substituting the known values of u, v, f, h and R.

Y Y’ P - ve + ve + ve X X’ - ve P - ve + ve X X’ Y Y’ Direction of incident light P - ve + ve + ve X X’ - ve P Direction of incident light - ve + ve X X’ Y Y’

Mirror Formula Magnification u – object distance v – image distance f – focal length of the mirror 1 v f + = u Magnification Magnification produced by a mirror is defined as the ratio of the size of the image to the size of the object. m = h’ h Magnification produced by a mirror is also defined as the ratio of the image distance to object distance. m = h’ h = - v u More of Reflection in Higher Class…