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Thin Lens Equation • Distances of virtual images are negative & distances of real images are positive. • Heights are positive if upright (above P.A.) and negative (below P.A.) • Converging lens has a real focal point (F) and a positive focal length (f) • Diverging lens has a virtual focal point (F) and a negative focal length (f) To remember which side of the lens the focal point should be, try to imagine where the focal point would be if the parallel rays of light passed through the lens. Magnification Equation • An upright image (above the P.A.) has a positive magnification. • An inverted image (below the P.A.) has a negative magnification. Practice Problem 1 An object 8.5 cm high is placed 28 cm from a converging lens. The focal length of the lens is 12 cm. Hint: is f + or −? a) Calculate the image distance b) Calculate the image height a) Givens: f = 12 cm ho = 8.5 cm do = 28 cm Required: a) di = ? b) hi = ? 1 1 1 f di do 1 1 1 di f do 1 1 1 di 12 28 1 7 3 di 84 84 1 4 di 84 4di 84 di 21cm The image is 21 cm from the lens and is a real image. b) hi di ho do hi ( 21) 8 .5 28 28hi 178.5 hi 6.4cm The height of the image is -6.4 cm. The image is inverted. Lens Application: The Telescope • For a very distant object, the incident rays that approach the objective lens of the telescope are *almost* parallel. • An intermediary real image is formed using an objective lens. This image then becomes the object for the next lens (ocular). • The light rays from intermediary image spread out until it reaches the eyepiece and enters the eye of observer. • Observer traces the rays to form a virtual inverted image of the original object. Lens Application: The Eye • Light enter the eye through the clear cornea which refracts it. • The pupil is a hole that allows light to pass through. The size of the pupil is controlled by the iris (coloured part of eye) muscles. • Eye has a converging lens that collects the light and refracts it to a focal point. Using its muscles, the lens can change the focal length to increase its focal power for very close objects. Image is formed on the retina (the screen) and is real & inverted. The optic nerve sends this information to the brain which then interprets it as right side up! Correcting Vision: Myopia • Nearsightedness • Can see objects up close but have difficulty with distant objects • Eyeball is too long relative to the focusing power of cornea/lens of eye. • Light ray focuses at a point before the retina rather than directly on the retina. • Use diverging lens so light rays can diverge more to reach the surface of retina in order for image to be formed. Correcting Vision: Hyperopia • Farsightedness • Can see distant objects but have difficulty with objects up close • Eyeball is too short relative to the focusing power of cornea/lens of eye. • Light ray focuses at a point beyond the retina rather than directly on the retina. • Use converging lens so light rays can converge earlier to reach the surface of retina in order for image to be formed. Correcting Vision: Astigmatism • Cornea and/or lens is not shaped correctly. • Image cannot be focused correctly and projected on the retina (or it is formed on more than one place on the retina). • Corrected using eyeglasses, contact (toric) lenses or laser eye surgery.