A diverging lens (f = -10 cm) is located 20.0 cm to the left of a converging len

Question

A diverging lens (f = -10 cm) is located 20.0 cm to the left of a converging lens (f = 32.0 cm). A 3.00 cm tall object stands to the left of the diverging lens, exactly at its focal point. (a) Determine the distance of the final image relative to the converging lens. . cm (b) What is the height of the final image (including proper algebraic sign)? NOT 124.53 7.38

Explanation / Answer

................********................… ..|..............*.....*...............… --|---11cm..--*...*------20 cm.--*-----*------> x (+ value) .................*.....*...............… ................********...............… Now use the formula 1/di + 1/do = 1/f where di is the distance from the lens to the image, do is the distance from the object to the lens, and f is the focal distance of the lens object is at focal point of lense means do = 11, and f = -11, so we get 1/di + 1/11 = -1/11 1/di = -2/11 ; or di = -11/2 = - 5.5 cm This means that the image formed by diverging lens with a real object will be virtual image and would be same side -5.5 cm from the centre. The magnification M of a lens is the ratio of the image size or height to the object height. A negative magnification signifies an inverted image. By this convention, a positive height indicates the arrow is erect and a negative height means the arrow is pointing down (valid for both object and image). M = hi / ho = -(di / do) hi / 3 = - (-5.5 / 11) = hi = 1.5 cm positive means pointing upwards since first lense is 20 cm away from second converging lense so total distance (di) for converging lense would be 25.5cm and we know f = 32 cm, so again 1/di + 1/do = 1/f 1/di + 1/25.5 = 1/32 1/di = 1/32 - 1/25.5 or di = -125.53 cm (from the center of converging lense) --------------Answer since distance is negative means left side of the lense or same side where object was Image will be virtual and magnifiaction would be hi / ho = -(di / do) hi / 1.5 = - (-125.53 / 25.5) or hi = 7.38 cm +ve means upward, (vertical), virtual image same side, at 125.53 cm

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