When light passes from a less dense to a more dense substance, (for example passing from air into water), the light is refracted (or bent) towards the normal.
A demonstration of refraction can be conducted at home in a dark room. All that is needed is a flashlight, a clear glass filled with water and a small mirror. Figure adapted from Ahrens, 1994
9. REFRACTION OF LIGHT Optically Rarer Medium And Optically Denser Medium Optical Density Versus Mass Density Do not get confused with optical density and mass density. Both are different from each other. While mass density is the ratio of mass per unit volume of a substance, optical density is the ratio of speed of light in one medium to another. For example, turpentine is optically denser than water as it has a greater refracting effect on light, but has a lower mass density than water. Cause For Refraction Of Light When a ray of light changes its medium, the basic change that occurs is the change in its wavelength. This change in the wavelength leads to the change in its velocity and the change velocity is responsible for its deviation; and hence, refraction takes place. Types Of Deviations1. When a ray of light travels from a rarer medium to a denser medium (Figure a), it bends towards the normal.2. When a ray of light travels from a denser medium to a rarer medium (Figure b), it bends away from the normal.3. If the incident ray falls normally (or perpendicularly) (Figure c) on the surface of a glass slab, then there is no bending of the ray of light and it goes straight.Since the incident ray goes along the normal to the surface, the angle of incidence in this case is zero (0°) and the angle of refraction is also zero (0°), i.e.∠i=∠r and ∠i=∠r=0° Note:1. When light travels from one medium to another, the frequency of light does not change. However, the velocity and the wavelength of light change. 2. When a ray of light passes from rarer to denser medium it bends towards the normal and ∠r<∠i . ∴ Angle of deviation, d = i – r 3. When a ray of light passes from denser to rarer medium, it bends away from the normal and ∠r>∠i. ∴ Angle of deviation d = r – i 4. A ray of light travelling along the normal passes undeflected. Terms Related To Refraction
i)Transparent surface 10.REFRACTIVE INDEX
We know that a ray of light travels obliquely from one transparent medium into another will change its direction in the second medium. The extent of the change in direction that takes place in a given pair of media is expressed in terms of the refractive index of the second medium with respect to the first medium. The refractive index can be linked to the relative speed of propagation of light in different media. μ21=sinisinr=Velocity of light inmedium1Velocityoflightinmedium2 If medium 1 is air or vacuum, then 1μ2 is called Absolute refractive index (μ) of medium 2. Relative Refractive Index KNOW MORE μ=cv=vλvλm or λm=λμ As light goes from rarer to denser medium, its wavelength decreases. 11. PRINCIPLE OF REVERSIBILITY OF PATH If a ray of light, after suffering any number of reflections or refractions has its path reversed at any stage, it travels back to the source along the same path in the opposite direction. This is called principle of reversibility. Let us now make use of the principle of reversibility of light to arrive at an important result. When ray of light travels from rarer to denser medium, the refractive index of denser medium with respect to rarer medium is given by μba=sin isin r….1, When the path angle of light is reversed, then r will be treated as angle of incidence and i will be treated as angle of refraction because the ray of light would now travel from denser to rarer medium. So, refractive index of rarer medium with respect to denser medium is given by μab=sin rsin i …(2)Multiplying (1) by (2), we get μba×b μa=sinisinr×sinrsini=1 (or) μba=1μab Conclusion: The refractive index of denser medium with respect to rarer medium is the reciprocal of the refractive index of rarer medium with respect to denser medium. 12. REFRACTION THROUGH A PARALLEL SLAB
Consider a ray of light AB passing from air (medium 1)through a parallel sided glass slab (medium 2) into air (medium 1). The ray of light will clearly suffer two refractions. Since the medium on both sides of glass is the same therefore, the ray of light will get laterally shifted without any deviation (Figure). This is proved below. we get, μga×μag=sini1sinr1×sini2sinr2 But we know, μba=1μab ∴ 1μab×μba=sin i1sin r1×sin i2sin r2 Since the slab is parallel sided ⇒ i2 = r1. ∴ sin i1sin r2=1 ⇒sin i1=sin r2 ⇒i1=r2 Conclusion : Lateral Shift Or Lateral Displacement Consider a parallel sided slab EFGH as shown in Figure such that EF is parallel to GH. A light ray AB passing from air through a parallel sided glass slab undergoing refraction and then entering the air again. The refracted and emergent ray are respectively BC and CD. The ray under goes refraction twice, one at the surface EF and other at the surface GH. but r1 = r2, so sin i2sin r1=μ ……..(3) From right angled triangle BCP, sinθ=CPBC , CP = BC sin θ where θ = i1 – r1 From right angled triangle BKC, cos r1=BKBC; BC=BKcos r1=tcos r1 ; ⇒ x=tsin i–cos icos r.sin r ⇒ x=t sin i1–cos icos r.sin rsin i ⇒x=t sin i1–1μcos icos r put cos r=1–sin2r=1–sin2iμ2 so x=t sin i1–1μcos i1–sin2iμ2; x=t sin i1–cos iμ2–sin2i In the approximation of small angle of incidence i with sin i= i and cos i= 1Lateral displacement is given as x=t i1–1μ ⇒ x= t iμ–1μ 13. SPHERICAL LENSES Similarly, a double concave lens is bounded by two spherical surfaces, curved inwards. It is thicker at the edges than at the middle. Such lenses diverge light rays and are called diverging lenses. A double concave lens is simply called a concave lens. Terms Related To Lenses Several rays of light parallel to the principal axis are falling on a concave lens. These rays after refraction from the lens, are appearing to diverge from a point on the principal axis. This point is called the principal focus of the concave lens. If you pass parallel rays from the opposite surface of the lens, you will get another principal focus on the opposite side. Letter F is usually used to represent principal focus. However, a lens has two principal foci. They are represented by F1 and F2. vii) The distance of the principal focus from the optical centre of a lens is called its focal length. The letter f is used to represent the focal length. KNOW MORE First Principal Focus And First Focal Length 14. IMAGE FORMATION BY LENSES (ii) A ray of light passing through a principal focus after refraction from a convex lens will emerge parallel to the principal axis. This is shown in Figure (a) below. A ray of light appearing to meet at the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis. This is shown in Figure (b) below. (iii) A ray of light passing through the optical centre of a lens will emerge without any deviation. This is illustrated in Figure (a) and (b) below. Image Formation By A Convex Lens
Image formed by a convex lens when the object is placed between the optical centre and the principal focus (object between O and F1) 4. The image is formed on the same side of the lens, behind the object. Applications 4. It is used to study biological specimens such as parts of the flower, etc. Case II: When the object is placed at the focus of a convex lens (object at F1) 4. The image is formed at infinity, on the other side of the lens. Case III: When the object is placed between F1 and 2F1. Characteristics of the image formed 1. The image is real.2. The image is inverted.3. The image is enlarged (or magnified). 4. The image is formed beyond 2F2, on the other side of the lens.Applications This type of image formation is used in film and slide projectors, when enlarged image of a small slide (or film) is formed on a screen. Case IV: When the object is at 2F1 Characteristics of the image formed 1. The image is real.2. The image is inverted.3. The image is of the same size as the object. 4. The image is formed at 2F2, on the other side of the lens.ApplicationsThis type of image formation is used in terrestrial telescope, for erecting the inverted image formed by the objective lens of the telescope. Case V: When the object is beyond 2F1 4. The image is formed between F2 and 2F2, on the other side of the lens.ApplicationsThis type of image formation is used in a photographic camera, where a small, real and inverted image of an object is formed on the film. Case VI: When the object is at infinity (such that the rays coming from it are parallel to the principal axis of the convex lens)Characteristics of the image formed 4. The image is formed at F2, on the other side of the lens.ApplicationsThis type of image formation is used in a burning glass. When the rays of the sun are focussed by the lens of the burning glass on a piece of paper, the paper catches fire. The lens of the burning glass focuses the heat radiations on the paper as a result of which, the temperature of the paper rises to its ignition temperature and it catches fire. Case VII:When the object is at infinity (such that the rays coming from it are not parallel to the principal axis of the convex lens) Characteristics of the image formed 4. The image is formed on the focal plane on the other side of the lens. Applications IMAGES FORMED BY A CONVEX LENS FOR VARIOUS POSITIONS OF THE OBJECT
Images Formed By A Concave Lens Case I : When the object is located at infinity (such that the rays coming from it are parallel to the principal axis)Characteristics of the image formed 4. The image is formed at FI; on the same side of the lens as the object. Case II: Characteristics of the image formed 4. The image is formed in the focal plane on the same side of the lens as the object.ApplicationsThis type of image formation is used in Galilean telescope, where concave lens acts as an eye lens. Case III: When the object is anywhere between the optical centre (O) and infinity.Characteristics of the image formed 4. The image is formed between the optical centre (O) and the principal focus (F1) on the same side of the lens. IMAGES FORMED BY A CONCAVE LENS FOR VARIOUS POSITIONS OF THE OBJECT
15. LENS FORMULA 1 V–1u=1f Magnification Produced By Lenses Magnification=Height of the imageHeight of the object=image distanceimage object=m=vu If the magnification ‘m’ has a positive value, the image is virtual and erect. On the other hand, if the magnification ‘m’ has a negative value, the image is real and inverted. Now, areal magnification of lens is ma=v2u2 Cartesian Sign Conventions For Lenses
According to the New Cartesian Sign Convention:1. Object should be taken on the left side to the lens.2. All distances are measured from the optical centre of the lenses.3. The distances measured in the direction of the incident light are taken as positive whereas the distances measured against the direction of the incident light are taken as negative. 4. The distances measured upwards and perpendicular to the principal axis is taken as positive whereas the distances measured downwards and perpendicular to the principal axis is taken as negative. Power Of A Lens Power of a lens is defined as the reciprocal of the focal length of the lens, expressed in metre. power =1f(in m) power =100f(in m)Unit of the power of a lens:The S.I unit of the power of a lens is dioptre, which is denoted by the letter D.Note: 1. One dioptre is the power of a lens whose focal length is one metre.2. The power of a lens can be measured directly by using an instrument called dioptremetre. It is used by opticians to measure the power of spectacle lenses. 3. A convex lens has a positive focal length. So, the power of a convex lens is considered to be positive and is written as +D. A concave lens has a negative focal length, so the power of a concave lens is considered to be negative and is denoted as –D. Power Of A Combination Of Lenses In optical instruments like camera, microscopes, telescopes, etc. a number of a lenses are combined together to increase the sharpness of the image. Updated on April 15, 2021 |