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1 Lenses & Prism c c h c. A transparent sbstance bonded by two sraces o deinite geometrical shape is called Lens. pond ish 2. A lens may be considered to be made p o a nmber o small prisms pt together. 3. Principal axis: The line joining the two centres o cratre o the spherical sraces constitting a lens is called principal axis. 4. adis o cratre: A doble conex lens or a concae lens is bonded by two spherical sraces which are parts o spheres. The centre o sch a sphere is called the centre o cratre and the distance rom this centre pto the spherical srace is called the radis o cratre. 5. Optic centre: When a ray o light incident on one srace o a lens meets the second srace o the lens ater reraction and passes throgh a particlar point on the principal axis inside the lens sch that the emergent ray is parallel to the incident ray, then that point on the axis is called optic centre (). 6. Principal ocs : When a narrow beam o light parallel to the principal axis strikes a lens, the rays ater reraction either ocs at a point (in the case o conex lens) or appear to dierge rom a ixed point on the principal axis (in the case o a concae lens) o the lens. This point is called principal ocs (F). 7. Focal length: The distance between the optical centre and the principal ocs is called ocal length (). F F F F 9

8. Types o images ormed with a conex lens Position o object Position o image Natre o image Application At ininity Point size; real; At F Astronomical inerted telescope Beyond 2F At 2F Between F and

Erecting lens o terrestrial telescope Projector Simple microscope 9.

2 8. Types o images ormed with a conex lens Position o object Position o image Natre o image Application At ininity Point size; real; At F Astronomical inerted telescope Beyond 2F At 2F Between F and 2F Between F and 2F At 2F Beyond 2F Diminished; real; inerted Same size; real; inerted Magniied; real; inerted At F At ininity eal Within the ocal length On the same side Magniied; irtal; erect amera Erecting lens o terrestrial telescope Projector Simple microscope 9. With a concae lens, irrespectie o the position o the object, the image is ormed on the same side as the object within the ocal length. It is always diminished, erect and irtal. 0. The shape o - graph in the case o a conex lens or concae mirror is a rectanglar hyperbola.. The shape o graph in the case o a conex lens or concae mirror is a straight line. 0

3 2. Lens ormlae + ; ; + m ; 3. eraction at cred sraces : μ 2 (+ m); (+ ) m μ μ2 + μ2 μ Where μ reractie index o the medim in which the object lies. reractie index o the medim on the other side o cred srace Sign conention is positie, i object aces conex srace radis o cratre o cred srace is negatie, i object aces concae srace is positie, i image is real (orms on the other side o the lens) is negatie, i image is irtal (orm on the same side o the lens) First principal ocs is the object point or which image point lies at ininity. ; Power o reracting srace is gien by and μ μ2 μ μ2 μ μ Second principal ocs is the image point or which object point lies at ininity. μ ; and 2 μ2 μ 2 2

4 Power o reracting srace is gien by 4. Lens maker s ormla is Where μ2 μ 2 μ2 ( μ ) 2 μ l μm μm 2 μ l reractie index o the material o lens and μ m srronding medim o the lens. This ormla is applicable or thin lens and or paraxial rays. 5. The ocal length o a plane glass plate is ininity. 2 reractie index o the 6. The reciprocal o ocal length o a lens measred in metres is called its ocal power (P). P 7. The nit o ocal power is dioptre. 00 (or) P in metres in cm 8. One dioptre is the ocal power o a lens o ocal length one metre. 9. When two thin lenses o ocal lengths and 2 are kept in contact and is the ocal length o the combination, then Doble onex, +e; 2 -e Doble oncae, -e; +e or P P + P 2. 2 onexo-concae, -e; -e 2 oncao-conex, +e; +e 2

5 20. When two thin lenses are separated by a distance d then d 2 + or d Or P P +P 2 P P 2 d. It acts as a glass slab i + 2 d. 2. I a doble conex lens is ertically ct into two pieces, each piece will hae a ocal length eqal to twice the original. 22. I a conex lens o ocal length is broken into two semicirclar pieces, each piece will hae a ocal length. 23. An air bbble in water behaes like a diergent lens (i.e., concae lens) 24. I a conex lens o ocal length made o glass ( μ.5) is immersed in water ( μ 4/3), its ocal length becomes 4. The ocal power decreases by a actor I a glass lens is immersed in a liqid o the same reractie index, it disappears and does not act like a lens. i.e., the lens will hae ininite ocal length or zero ocal power. 26. A conex lens immersed in a liqid o reractie index greater than the reractie index o the lens behaes like a concae lens. 27. I a planoconex lens o radis o cratre and o ocal length is silered on the plane srace, it acts like a concae mirror o ocal length or 2 2( μ ) 28. I a planoconcae lens o radis o cratre and o ocal length is silered on the plane srace, it acts like a conex mirror o ocal length or 2 2( μ ) 29. I a planoconex lens o radis o cratre and o ocal length is silered on the cred srace, it acts like a concae mirror o ocal length 30. PISM / 2μ. a) A prism is a piece o gas or any other transparent material, bonded by two trianglar and three rectanglar sraces... A d i r r 2 d i 2 B 3 i

6 b) When a light ray passes throgh a prism it bends towards the base o the prism. c) The angle made by emergent ray with incident ray is called angle o deiation (d). d) di +i 2 A, Ar +r 2 where i angle o incidence, i 2 angle o emergence, A angle o prism, r angle o reraction at irst retracing ace, r 2 angle o reraction at second reracting ace. e) As the angle o incidence increases, angle o deiation irst decreases to a minimm ale (D) and then increases. ) I dd, then i i 2 i and r r 2 r g) D 2i A, A 2r A + D sin 2 μ A sin 2 h) The prism whose angle is ery small is called thin prism. i) For a thin prism D ( μ ) A. 3. eraction throgh a prism A angle o the prism or reracting angle D angle o deiation i, i 2 are the angles o reraction i. Angle o prism, Ar +r 2 ii. Angle o deiation Di +i 2 A iii. eractie index o the prism, 32. Limiting angle o the prism sini sini2 μ sinr sinr2 a) It is the angle o the prism or which a ray grazing on one o the ace o the prism ater reraction grazes ot rom the second ace. b) In this case i i 2 90, r r 2 As Ar +r 2 A2 4

7 c) μ sin sin(a / 2) d) Angle o deiation, Di +i 2 A D Deiation in a small angled prism : a) From Snell s law sin i μ sin r and sin i 2 μ sin r 2 For a small angled prism, i, i 2, r and r 2 are small i μ r and i 2 μ r 2 d(i +i 2 ) A μ (r +r 2 ) A μ A A d( μ )A b) As μ > μ. Thereore the deiation or iolet color is more than the deiation or red color (d >d r ). c) For a gien color o light the deiation increases as the angle o the prism increases. d) For a gien monochromatic light d A. d2 A 2 e) In case o thin prism, the angle o minimm deiation, d m ( μ ) A. 5

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Marketed and Distributed by FaaDoOEngineers.com REFRACTION OF LIGHT GUPTA CLASSES For any help contact: 995368795, 968789880 Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: 995368795, 968789880 Reraction o light:. The ratio o the sine o