REFRACTION OF LIGHT-2

REFRACTION OF LIGHT-2 : REFRACTION OF LIGHT-2 LECTURE BY: PROF. ARDAMAN SIDHU H.K.SIDHU INSTITUTE OF SCIENCES. hksidhuinstitute@gmail.com 09814123632 IN COLLABORATION WITH WIZIQ.COM

REFRACTION OF LIGHT-2L9/AS 23,JULY,09 7.00-P.M. : REFRACTION OF LIGHT-2L9/AS 23,JULY,09 7.00-P.M. REFRACTION AT SPHERICAL SURFACE. REFRACTION BY LENS. POWER OF A LENS. COMBINATION OF THIN LENSES IN CONTACT.

SPHERICAL REFRACTING SURFACES : SPHERICAL REFRACTING SURFACES A refracting surface which forms a part of a sphere of transparent refracting material is called a spherical refracting surface.

SPHERICAL REFRACTING SURFACES : SPHERICAL REFRACTING SURFACES There are two types of spherical refracting surfaces: Convex spherical refracting surface, which is convex towards rarer medium side as shown in Figure

SPHERICAL REFRACTING SURFACES : SPHERICAL REFRACTING SURFACES Concave spherical refracting surface which is concave towards the rarer medium side .

SPHERICAL REFRACTING SURFACES : SPHERICAL REFRACTING SURFACES New Cartesian Sign Conventions All distances are measured from the pole of the spherical refracting surface. The distance measured in the direction of incidence of light are taken as positive and the distances measured in a direction opposite to the direction of incidence of light are taken as negative.

Assumptions: : Assumptions: For refraction at spherical refracting surfaces, assumptions are: The object consists only of a point lying on the principal axis of the spherical refracting surface. The aperture of spherical refracting surface is small. The incident and refracted rays make small angles with the principal axis of the surface, so that sin

Slide 8 : (a) Real Image Let a spherical refracting surface XY separate a rarer medium of refractive index ?1 from a denser medium of refractive index ?2.

REFRACTION FROM RARER TO DENSER MEDIUM : REFRACTION FROM RARER TO DENSER MEDIUM The surface is convex towards rarer medium side. Consider a point object O lying on the principal axis of the surface, Fig. Shown. A ray of light starting from O and incident normally on the surface XY along OP passes straight . Another ray of light incident on XY along OA at ?I is refracted along AI at ?r, bending towards the normal CAN. The two refracted rays actually meet at I, which is the real image of O.

REFRACTION FROM RARER TO DENSER MEDIUM : REFRACTION FROM RARER TO DENSER MEDIUM From A, draw AM ? OI. Let ?AOM = And As external angle of a triangle is equal to sum of internal opposite angles, therefore, in ?IAC Similarly, in ? OAC, ..(1) i = …(2)

Slide 11 : According to Snell’s law, ..(3) ( angles are small ) Using (1&2), we get, As angles are small, using we get As aperture of the spherical surface is small, M is close to P. Therefore, MO PO=MO, MI

REFRACTION FROM RARER TO DENSER MEDIUM : REFRACTION FROM RARER TO DENSER MEDIUM From (4), Using new Cartesian sign conventions, we put PO = - u, PI = + v, PC = R …(5) This is the required relation.

REFRACTION FROM DENSER TO RARER MEDIUM : REFRACTION FROM DENSER TO RARER MEDIUM At A convex spherical surface. Let P be the pole and C be the centre of curvature of a spherical refracting surface XY, In given figure This surface is convex towards the rarer medium and separates a denser medium of refractive index from a rarer medium of refractive index

REFRACTION FROM DENSER TO RARER MEDIUM : REFRACTION FROM DENSER TO RARER MEDIUM Let O be a point object lying on the principal axis of the spherical surface. A ray of light OA starting from O meets the refracting surface at A. On refraction, it bends away from the normal CAN and moves along AI. Another ray of light OP falling normally on the refracting surface goes undeviated along PI. The two refracted rays AI and PI actually meet at I, which is, therefore, the real image of the point object O

REFRACTION FROM DENSER TO RARER MEDIUM : REFRACTION FROM DENSER TO RARER MEDIUM . If i and r are the angles of incidence and refraction, then from Snell’s law, we have As I and r are small, sin and ….(6)

REFRACTION FROM DENSER TO RARER MEDIUM : REFRACTION FROM DENSER TO RARER MEDIUM ?from (6), From A, draw AM perpendicular to OI As angles are small, using ? = we get,

REFRACTION FROM DENSER TO RARER MEDIUM : REFRACTION FROM DENSER TO RARER MEDIUM Since aperture of the refracting surface is small, M is close to P. ? MC PC, MO PO, Applying new Cartesian sign conventions, PO = -u, PI + v, PC = - R …(7)

LENSES : LENSES A lens is a portion of a transparent refracting medium bound by two spherical surfaces or one spherical surface and the other plane surface. Lenses are divided into two classes: - Convex or convergent lenses, and Concave or divergent lenses.

Convex or convergent lenses : Convex or convergent lenses Double convex lens Fig.(ii) Plano convex lens, Fig.(i) Concavo convex lens, Fig. (iii)   For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com

Concave or Diverging lenses. : Concave or Diverging lenses. Double concave lens Fig.(ii) Plano concave lens. Fig (i) Convexo concave lens Fig. (iii)

Some important terms related to lenses: : Some important terms related to lenses: Principal axis. It is defined as a straight line passing, through the centers of curvatures of two surfaces of a lens. Optical centre. For a thin lens, however, the optical centre is taken as a point lying on the principal axis so that a ray of light passing through it does not suffer any deviation from its path Principal Focus. Aperture. Aperture of a lens is the effective diameter of its right transmitting area.

LENS MAKER’S FORMULA : LENS MAKER’S FORMULA Lens Maker’s formula is a relation that connects focal length of a lens to radii of curvature of the two surfaces of the lens.

New Cartesian Sign Conventions : New Cartesian Sign Conventions All distances are measured from the optical centre of the lens. All the distances measured in the direction of incidence of light are taken as positive, whereas all the distances measured in a direction opposite to the direction of incidence of light are taken as negative. For a convex lens, f is positive and for a concave lens, f is negative, as is clear from fig. above.

Slide 24 :

Derivation of lens maker’s formula for convex lens. : Derivation of lens maker’s formula for convex lens. A convex lens is made up of two convex spherical refracting surfaces. The final image is formed after two refractions in Fig. Shown.P1, P2 are the poles,, C1, C2 are the centers of curvature of two surfaces of a thin convex lens XY with optical centre at C, Let ?1 be the refractive index of the rarer medium around the lens.

Derivation of lens maker’s formula for convex lens. : Derivation of lens maker’s formula for convex lens. Consider a point object O lying on the principal axis of the lens. A ray of light starting from O and incident normally on the surface XP1Y along OP1 passes straight. Another ray incident on XP1Y along OA is refracted along AB. If there were no boundary/ second surface XP2Y of the lens, the refracted ray AB would go straight meeting the first refracted ray at I1. Therefore, I1 would have been a real image of O formed after refraction at XP1Y.

LENS MAKER FORMULA : LENS MAKER FORMULA Actually, the lens material is not continuous. Therefore, the refracted ray AB suffers further refraction at B and emerges along BI, meeting actually the principal axis at I. Therefore, I is the final real image of O, formed after refraction through the convex lens. For refraction at the second surface XP2Y, we can regard I1 as a virtual object, whose real image is formed at I.

LENS MAKER FORMULA : LENS MAKER FORMULA Let R2 be radius of curvature of second surface of the lens. As refraction is now taking place from denser to rarer medium, therefore, using eqn(7), we get.

LENS MAKER FORMULA : LENS MAKER FORMULA Adding (8) and (9), we get Put refractive index of material of the lens w.r.t. surrounding medium. When object on the left of lens is at ?, image is formed at the principal focus of the lens.

LENS FORMULA : LENS FORMULA It is a relation between focal length of a lens and distance of object and image from optical centre of the lens. CONVEX LENS. The image formed may be real or virtual. Real Image Let C be the optical centre and F be the principal focus of a convex lens of focal length CF=f. AB is an object held perpendicular to the principal axis of the lens at a distance beyond focal length of the lens. A real, inverted and magnified image A’ B’ is formed

LENS FORMULA : LENS FORMULA as shown in Fig. As and ABC are similar.

LENS FORMULA : LENS FORMULA Using New Cartesian Sign Conventions, let

LINEAR MAGNIFICATION PRODUCED BY A LENS : LINEAR MAGNIFICATION PRODUCED BY A LENS The linear magnification produced by a lens is defined as the ratio of the size of the image (h2) to the size of the object (h1). It is represented by m.

LINEAR MAGNIFICATION PRODUCED BY A LENS : LINEAR MAGNIFICATION PRODUCED BY A LENS Thus In a convex lens, when image formed is real, Fig. Thus in a convex lens, linear magnification is positive, in which image formed is virtual and linear magnification is negative, when image formed is real. In a concave lens, image formed is always virtual.i.e. linear magnification in case of a concave lens is always positive.

POWER OF A LENS : POWER OF A LENS Power of a lens is defined as the ability of the lens to converge a beam of light falling on the lens. It is measured as the reciprocal of focal length of the lens.

POWER OF A LENS : POWER OF A LENS According to lens maker’s formula, For a converging lens, power is taken as positive and for a diverging lens, power is taken as negative. The SI unit of power is dioptre (D) When Hence one dipotre is the power of a lens of focal length one meter.

COMBINATION OF THIN LENSES IN CONTACT : COMBINATION OF THIN LENSES IN CONTACT In various optical instruments, two or more lenses are combined to increase the magnification of the image. Make the final image erect w.r.t. the object. To remove aberration in lens.

FOCAL LENGTH OF EQUIVALENT LENS : FOCAL LENGTH OF EQUIVALENT LENS Both the lenses are convex Let C1, C2 be the optical centers of two thin convex lenses L1 and L2 held co-axially in contact with each other in air. Suppose f1 and f2 are their respective focal lengths. Fig. show. Distance OC1=u. The lens L1. alone would, form its image at I’ where C1 I’ = v’ …(16) From the lens formula,

FOCAL LENGTH OF EQUIVALENT LENS : FOCAL LENGTH OF EQUIVALENT LENS I’ would serve as a virtual object for lens L2, which forms a final image I at distance C2 I = v, As the lenses are thin, therefore, for the lens L2, i.e. u = C2 I’ = C1 I’ = v’ From the lens formula for L2, …(17)

FOCAL LENGTH OF EQUIVALENT LENS : FOCAL LENGTH OF EQUIVALENT LENS Adding (16) and (17), we get …(18) Let the two lenses be replaced by a single lens of focal length F, which forms image I at distance v, of an object at distance u from the lens. For this lens, From (18) we get

Slide 41 : For all your Physics Problems Call me at……………9814123832 Email ………………. hksidhuinstitute@gmail.com