LIGHT : REFLECTION AND REFRACTION
Light is a form of electromagnetic radiation that causes the sensation of sight. It is an indispensable tool without which we cannot explore the colorful beauty of nature.The blue sky, the rainbow, the red of the sunrise and sunset, the twinkling of stars, the radiance of sparkling diamonds and pearls, and shining color of gems are just some of the natural wonders of light and color.
NATURE OF LIGHTLight is an electromagnetic wave.These waves do not require any medium for their propagation.The wavelength of visible light waves is very small, only about 4 x 10-7m to 8 x 10-7mThe speed of light wave depends on the nature of the medium through which they pass.The speed of light waves in vacuum is very high, being 3 x 108 m/s.
Light provides us means of communication. The fibre-optic cables consisting of many glass fibres transmit hundreds of telephone conversations over long distances.
REFLECTION OF LIGHT
When light falls on the surface of an object, it may bei) absorbedii) transmitted iii) reflectedWhen light falls on the surface of an object, some of it is sent back. The process of sending back the light rays which fall on the surface of an object, is called reflection of light.
An image is formed when the light rays coming from an object meet ( or appear to meet) at a point, after reflection from a mirror ( or refraction from a lens).Real Image If the light rays actually meet after reflection or refraction is called real image. It can be obtained on a screen.Virtual Image If the light rays appear to meet after reflection or refraction, then it is called virtural image. It cant be obtained on a screen.
LAWS OF REFLECTION OF LIGHT
FIRST LAW The angle of incidence (i) is equal to the angle of reflection (r ) SECOND LAW The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.
FORMATION OF IMAGE IN A PLANE MIRRORThe characteristics of image formed in a plane mirror are i) image is virtual ii) image is erect iii) image is of the same size of the object. iv) image is formed as far behind the mirror, as the object is in front of it. v) image is laterally inverted.
A spherical mirror is that mirror whose reflecting surface is the part of a hollow sphere of glass. It is of two types :i) concave mirrors ii) convex mirrors
RULES FOR FORMATION OF IMAGE BY SPHERICAL MIRRORSWhen an object is placed before a spherical mirror, an image is formed. The image is formed at that point where at least two reflected rays intersect (or appear to intersect).
Now to find out the position of an image formed by a concave mirror, only two rays light is required. We use those rays whose path is certain, the diagram formed in this way is called as ray diagram. Continued
To draw ray diagram, the following rules are used: i) A ray of light parallel to the principal axis of the mirror, passes through the focus after reflection from the mirror.ii) A ray of light passing from the center of curvature of the mirror is reflected back along the same path.iii) A ray of light passing through the focus of a concave mirror becomes parallel to the principal axis. An image of any point is formed at that point where at least two reflected rays intersect or appear to intersect.
IMAGE FORMATION BY CONCAVE MIRROR
position of the objectPosition of the imageSize of the imageNature of the imageAt infinity At the focus FHighly DiminishedReal and InvertedBeyond CBetween F and CDiminishedReal and InvertedAt CAt CSame sizeReal and InvertedBetween C and FBeyond CEnlargedReal and InvertedAt FAt infinityHighly enlargedReal and InvertedBetween P and FBehind the mirrorEnlarged Virtual and irect
IMAGE FORMATION BY CONVEX MIRROR
Position of the objectPosition of the imageSize of the imageNature of the imageAt infinityAt the focus F, behind the mirrorHighly diminished, point sizeVirtual and erectBetween infinity and the pole of the mirrorBetween p and F, behind the mirrordiminishedVirtual and erect
NEW CARTESIAN SIGN CONVENTIONHeight downwards (-ve)Direction of Incident lightIncident light (-ve)Direction againstDistance alongIncident light (+ve)Height upwards (+ve)Height downwards (-ve)Height downwards (-ve)Objects on the leftNMPXXYYBAAB
MIRROR FORMULAABCPMNABhhFRfvFig 2.3u
FORMATION OF IMAGE BY CONVEX MIRRORABMNCEDABFP
We will now obtain a relation between the object-distance (u), the image distance (v) and the focal length (f) of the spherical mirror having small aperture (much less than the radius of curvature (R). This relation is called Mirror Formula. It remains the same in all types of physical situations, whether the image is real or virtual
We now derive the mirror formula for a concave mirror producing a real image in fig 2.3.When the object AB is of size or height (h) is placed on the left in front of the concave mirror MN, beyond its centre of curvature C, The image formed is real, inverted and diminished in size (h)
Using the New Cartesian Sign Convention, we have Object distance = PB = - u Image distance = PB= -vFocal length = PF = -fRadius of curvature = PC = -RNow in fig 2.3 , the right angle triangles ABP and ABP, are similar, so that AB PB -v v AB PB -u u3,1
Similarly in the right angled triangles, ABC and ABC are similar, so that AB CB AB CBAs we measure all distances from the pole P, we have CB = PC PB CB = PB PCUsing equation 3.2 we getAB PC PB (-R)-(- v) -R + vAB PB PC (-u)(-R) -u + R3.3
Comparing Eqs. (3.1) and (3.3), we get - R + v v - u + R uOr, uR + vR = 2uvDividing both sides by uvR, we get1/v + 1/u = 2/R -------------- (3.4)When the object AB is taken at a very large distance ( at infinity), as shown the image is formed at the focus F. Thus, when u = , v = f, putting the values in eq 3.4 , we get1/f + 1/ = 2 / R or f = R/2 ------ (3.5)
MAGNIFICATIONThe ratio between the height of the image produced by the spherical mirror to the height of the object is called linear magnification.
Height of the imageLinear magnification = -------------------------- Height of the objecthi M = ---------= v/uho
REFRACTION OF LIGHT AND ITS LAWSthe ratio of sine of angle of incidence to the sine of angle of refraction is constant. Thus, angle of incidence I and the angle or refraction r are related as Sin i------- = n21sin r n21 is a constant and is called the refractive index of second medium with respect to first medium. It is also known as Snells law of refraction.ii) The incident ray, the refracted and the normal at the point of incidence lie in the same plane.
REFRACTIVE INDEXAns:- For two media and for a light of a particular color, the ratio of sine of incidence angle and sine of refraction angle is called refractive index of second medium with respect to first.Sin i--------------------- = n21sin rif motion of light is in reverse direction means from medium 2 to medium 1, refractive index is reversiblen12 = sin r/ sin i = 1/n21if velocity of light is v1 in first medium and v2 in second medium, n21 = velocity of light in first medium(v1)/ velocity of light in second medium (v2)
Refractive index of water is 4/3 and glass is 3/2 with respect to air. What is refractive of glass with respect to water.
Ans;- refractive index of air , n1 = 1.00 Thus, refractive index of water w.r.t. air, n21 = n2 = 4/3Refractive index of glass w.r.t. air = n31 = n3 = 3/2Refractive index of glass w.r.t water = n32 n32 = n31 x n12 = n31/ n21 = n3/n2 = (3/2)/(4/3) = 9/8 = 1.125
RULES FOR IMAGE FORMATION IN SPHERICAL LENSESA ray from the object parallel to the principal axis after refraction passes through the second principal focus F2 ( in a convex lens) or appears to diverge ( in a concave lens) from the first principal focus F1A ray of light passing through the first principal focus ( in a convex lens), or appearing to meet at it ( in a concave lens) emerges parallel to the principal axis after refraction.
3) A ray of light passing through the optical centre of the lens, emerges without any deviation after refraction.
IMAGE FORMATION BY CONVEX LENS
position of the objectPosition of the imageSize of the imageNature of the imageAt infinity At the focus F2Highly DiminishedReal and InvertedBeyond 2F1Between F2 and 2F2DiminishedReal and InvertedAt 2F1At F2Same sizeReal and InvertedBetween F1 and 2F1Beyond 2F2EnlargedReal and InvertedAt F1At infinityHighly enlargedReal and InvertedBetween F1 and OOn the same side of lensEnlarged Virtual and irect
IMAGE FORMATION IN CONVEX LENSCONVEX LENSANMF12F1BCABAF2O
Here object distance = OB = -uImage distance = OB = vFocal length = OF2= f AB = OC ABO ~ ABO are similarAB/AB = OB/OB = v/-u .eq. (i)Similarly OCE2 ~ ABF2AB/OC = F2B/OF2, As AB = OC, thenAB/AB = F2B/OF2 = ( OB- OF2)/OF2 = (v-f)/f ..eq. (ii)
From eq. (i) & (ii) we get, -v/u = v-f/fOn cross multiplication and dividing both sides by uvf, we get,
1/v 1/u = 1/f
IMAGE FORMATION IN CONCAVE LENSObject is at infinity and the image is at F1OF12F1
When the object is between O and InfinityBA2F1F1A'BO
Image formation in concave lens
Position of the objectPosition of the imageSize of the imageNature of t