Physics

PHS 5041 Optics Lenses

Lenses are transparent objects with at least one curved surface. Lenses can be: _Convex or converging (***thickest at the centre) (double convex, plano-convex, concavo-convex) _Concave or diverging (double concave, plano-concave, convexo-concave

PHS 5041 Optics Lenses

XY: principal axis of lens O: optical centre of lens F: principal focus of length F’: secondary principal focus of length OF or OF’: focal length

PHS 5041 Optics Lenses Lenses behave like prims, but with varying incident angles

PHS 5041 Optics Lenses Lenses behave like prims, but with varying incident angles

PHS 5041 Optics Lenses Principal rays: Rays for which we do not need to measure angle in order to determine their direction after reflection. There are 3 types of principal rays (converging lens) 1: Incident ray parallel to principal axis 2: Incident ray passing through secondary focus 3: Incident ray passing through optical centre

PHS 5041 Optics Lenses

Drawing images formed by lenses: We use the three principal rays (whenever feasible) for both type of lenses, and according to the position of the object

PHS 5041 Optics Lenses Drawing images (Converging lenses): ***When the object is at infinity, the image is a dot, and it is located at F (principal focus of length) Object between ∞ and 2F’, Image is: _Real _Between F and 2F _Inverted _Smaller

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object at 2F’, Image is: Real, at 2F, Inverted, Same size

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object between 2F’ and F’, Image is: Real, after 2F, Inverted, Larger

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object at F’, NO Image

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object between F’ and O, Image is: Virtual, between F’ and O, Upright, Larger

PHS 5041 Optics Lenses Drawing images (Converging lenses):

PHS 5041 Optics Lenses Drawing images (Converging lenses): Converging lenses DO NOT produce images between F and O

PHS 5041 Optics Lenses Practice: _The image of a slide on a screen is larger, upright and real (seen on screen). a)Should the slide be upright or inverted when placed in the projector? b)Where should the slide be located with respect to the lens? c)Where should the screen be placed with respect to the lens? Inverted Between F’ and 2F’ Between 2F and ∞

PHS 5041 Optics Lenses Practice: _To photograph an object located at infinity, should the principal focus of the lens be located in front, behind or on the film? Hint: the film is the screen. _To photograph an object close to the camera, should the principal focus of the lens be located in front, behind or on the film? Hint: the film is the screen. F should be located on the film(object-lens- F/film), for objects at infinity produce images at F F should be located in front of the film (object-lens-F- film), for converging lenses do not produce images between F and lens produce images at F

PHS 5041 Optics Lenses Principal rays: Rays for which we do not need to measure angle in order to determine their direction after reflection. There are 3 types of principal rays (diverging lens) 1: Incident ray parallel to principal axis 2: Incident ray directed to the secondary focus 3: Incident ray passing through optical centre

PHS 5041 Optics Lenses

Drawing images (Converging lenses): ***When the object is at infinity, the image is a dot, and it is located at F (principal focus of length) Object between ∞ and F, Image is: _Virtual _Between F and O _Upright _Smaller

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object at F, Image is: Virtual, between F and O, Upright, Smaller

PHS 5041 Optics Lenses Drawing images (Converging lenses): Object at F and O, Image is: Virtual, between F and O, Upright, Smaller

PHS 5041 Optics Lenses Drawing images (Converging lenses): Diverging lenses ONLY produce images between F and O

PHS 5041 Optics Lenses Images (Converging lenses): _Never between F and O _Real, inverted, and behind lens (converging refracted rays) _Virtual, upright, in front of lens (diverging refracted rays) _No image (parallel diffracted rays) Images (Diverging lenses): _Always between F and O _Always upright, virtual and smaller _Object moving from infinity, images grows from dot at F to same size very near to lens

PHS 5041 Optics Lenses Calculations:

PHS 5041 Optics Lenses Example: An object 1cm high is placed 27 cm from a convex lens with focal length of 18 cm. At what distance from the mirror is the image formed and what is the height, type and orientation?

PHS 5041 Optics Lenses Example: An object 1cm high is placed 27 cm from a convex lens with focal length of 18 cm. At what distance from the mirror is the image formed and what is the height, type and orientation?

PHS 5041 Optics Lenses Optical power: Capacity of a lens to bend light rays L1L1 L1L1 L3L3 Proportionality between f and P?

PHS 5041 Optics Lenses Optical power: Capacity of a lens to bend light rays P = 1 / f P: Optical power (d: diopters) f: focal length (m: meters) P > 0 (converging lens) P < 0 (diverging lens)

PHS 5041 Optics Lenses Optical power of a system of lenses: P t = P 1 + P 2 + … + P n P: Optical power (d: diopters) f: focal length (m: meters) P t > 0 (converging system of lens) P t < 0 (diverging system of lens) n lenses

PHS 5041 Optics Lenses Example: Find the optical power of a system of lenses whose individual focal lengths are 0.20 m, 0.10 m and -0.05m respectively. Is the system of lenses converging or diverging? P = 1/fP t = P 1 + P 2 + P 3 P 1 = 1 / 0.20m P t = 5d + 10d – 20d P 1 = 5d P 2 = 1 / 0.10m P t = - 5d (Diverging system, P < 0) P 2 = 10d P 3 = 1 / -0.05m P 3 = -20d

PHS 5041 Optics Lenses Lens maker equation: P = (n – 1) (1 / R / R 2 ) P: Optical power (d: diopters) n: index of refraction of lens material R 1 & R 2 : radii of curvature of each side of the lens (m: meters) R 1 & R 2 > 0 (converging lenses) R 1 & R 2 < 0 (diverging lenses) P > 0 (converging lens) P < 0 (diverging lens)

PHS 5041 Optics Lenses Example: A plastic lens with index of refraction 1.51 is composed of two convex lenses with radius of curvature 5 cm on each side. Find the optical power of a system of lenses. Is the system of lenses converging or diverging? P = (n – 1) (1 / R / R 2 ) P = (1.51 – 1) (1 / 0.05m + 1 / 0.05m) P = (0.51) (40) d P = 20.4 d (Converging system, P > 0)

PHS 5041 Optics Lenses Human eye: _Sclerotic: opaque membrane that protects the eye _Cornea: transparent membrane _Lens: converging lens _Ciliary muscles: Exert pressure on lens, thus changing its F (accommodation). This allows for near and distant vision _Retina: back of the eye (screen)

PHS 5041 Optics Lenses Nearsightedness (Myopia): Difficulty seeing distant objects Possible causes: _Eyeball is too long _Cornea is too curved Evidence: Image is formed in front of the retina Correction: Eyeglasses or contact glasses with diverging lenses

PHS 5041 Optics Lenses Farsightedness (Hyperopia): Difficulty seeing nearby objects Possible causes: _Eyeball is too short Evidence: Image is formed behind the retina Correction: Eyeglasses or contact glasses with converging lenses

PHS 5041 Optics Lenses Presbyopia: Difficulty adjusting the focal length of lens (due to aging) Possible causes: _Ciliary muscles lose some of their elasticity Evidence: Image is formed behind the retina Correction: Eyeglasses or contact glasses with converging lenses

PHS 5041 Optics Lenses Astigmatism: Difficulty focusing on both plans (horizontal and vertical) at the same time Possible causes: _Differences in curvature of the lens of the eye Evidence: Eye focuses better in one plane than in the other Correction: Eyeglasses with cylindrical lenses

PHS 5041 Optics Lenses Other defects Strabismus: Misalignment of eyeballs. Prevents combination of images formed by both eyes Pigmentary glaucoma: Excessive pressure in liquid substances of eyeball. Destroys optic nerve, leads to blindness Cataracts: Lens becomes opaque. People cannot see near or distant objects (need bifocals: diverging and converging lenses) Colour blindness: Rods in the retina are insensitive to colours.