LensesLenses are made of transparentmaterials, like glass or plastic.Each of a lens’ two faces is part of asphere and can be convex or concaveIf a lens is thicker at the center than theedges, it is a convex, or converging, lenssince parallel rays will be converged tomeet at the focus. A lens which is thinner in the centerthan the edges is a concave, or diverging,lens since rays going through it will bespread out.Convex(Converging) LensConcave(Diverging) Lens
Lenses and Images Light rays that enter a converging lens parallel to its axis bendto meet at a point called the focal point. The distance from the center of the lens to the focal point iscalled the focal length. The optical axis usually goes through the center of the lens.
The image formed by a lens A lens can form a virtual image just as a mirror does. Rays from the same point on an object are bent by the lens sothat they appear to come from a much larger object.
A converging lens can also form a real image. In a real image, light rays from the object actually come backtogether.The image formed by a lens
Drawing ray diagrams A ray diagram is the best way to understand what type ofimage is formed by a lens, and whether the image ismagnified or inverted. These three rays follow the rules for how light rays are bentby the lens:1. A light ray passing through the center of the lens is notdeflected at all (A).2. A light ray parallel to the axis passes through the far focalpoint (B).3. A light ray passing through the near focal point emergesparallel to the axis (C).
Convex Lens: Object Beyond 2F•• • •F F 2F2FobjectimageThe image formed whenan object is placedbeyond 2F is locatedbehind the lens betweenF and 2F. It is a real,inverted image which issmaller than the objectitself.Experiment with this diagram
Convex Lens: Object Between 2F and F•• • •F F 2F2FobjectimageThe image formedwhen an object isplaced between 2F andF is located beyond 2Fbehind the lens. It is areal, inverted image,larger than the object.
Convex Lens: Object within F•• • •F F 2F2FobjectimageThe image formed when an object is placed in front of F islocated somewhere beyond F on the same side of the lens asthe object. It is a virtual, upright image which is larger thanthe object.convex lens used as a magnifier
Concave Lens Diagram•• • •F F 2F2FobjectimageNo matter where the object is placed, the image will be on the sameside as the object. The image is virtual, upright, and smaller thanthe object with a concave lens.Experiment with this diagram
Sign convention for spherical lenses The sign convention for spherical lenses is the same as inspherical mirrors except that the distances are measured from theoptical centre (O). The focal length of a convex lens is positive ( + ve ) and thefocal length of a concave lens is negative ( - ve ).Direction of incident lightDistance towards the left (- ve )Heightdownwards ( - ve )Heightupwards ( + ve )Convex lensObjectImageODistance towards the right ( + ve )
Thin lens formula The thin lens formula is a mathematical way to do raydiagrams with algebra instead of drawing lines on graphpaper.1 + 1 = 1o i ffocallength (cm)Image distance(cm)Objectdistance(cm)
Derivation of Lens Formula (Convex Lens)Let AB represent an object placed at right angles to the principalaxis at a distance greater than the focal length f of the convex lens.The image A1B1 is formed beyond 2F2 and is real and inverted.OA = Object distance = uOA1 = Image distance = vOF2 = Focal length = fC C
OAB and OA1B1 are similarA1B1A B=O A1O A------------------- (1)Similarly , OCF2 and F2A1B1 are similarA1B1O C=F2A1O F2C CBut we know that OC = ABthe above equation can be written as
C CA1B1A B=F2A1O F2------------------- (2)From equation (1) and (2), we getO A1O A= F2A1O F2= OA1 – OF2O F2v-u= v – ffOrv f = - u v + u f ------------------- (3) Dividing Both side by uvf1u=-1f+1vOr1f=1v1u–
The magnification M of an image is the ratio of the height ofthe image to the height of the object:M =Image heightObject heightThis number is a dimensionless ratio (a length over a length)and does not have any unitsRule: The magnification factor M of a lens is always positiveand given by:M =vuImage heightObject heightMagnification of a lens
Power of a lensThe power of a lens is the reciprocal of its focal lengthThe SI unit of power is dioptre (D).1 dioptre is the power of a lens whose focal length is 1 meter.The power of a convex lens is positive ( + ve ) and the power of aconcave lens is negative ( - ve ).)(1mfPPf10r
Optical Systems An optical system is a collection of mirrors, lenses, prisms,or other optical elements that performs a useful functionwith light. Characteristics of optical systems are:– The location, type, and magnification of the image.– The amount of light that is collected.– The accuracy of the image in terms of sharpness, color,and distortion.– The ability to change the image, like a telephoto lens on acamera.– The ability to record the image on film or electronically.
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