An object is located to the left of a convex lens whose focallength is 35 cm. Th

Question

An object is located to the left of a convex lens whose focallength is 35 cm. Themagnification produced by the lens is m = 3.0.
(a) To increase the magnificationto 4.5, should the object bemoved closer to the lens or farther away?

(b) Calculate the magnitude of the distance through which theobject should be moved.
(a) To increase the magnificationto 4.5, should the object bemoved closer to the lens or farther away?

(b) Calculate the magnitude of the distance through which theobject should be moved.

Explanation / Answer

. 1.   Lens equation: 1/f = 1/p +1/q   ;   where:   f =focal length      p = distance toobject      q = distance toimage 2.   magnification = q/p 3.   f < 0 for diverging lens ormirrors . 4.   3 =q/p   ;   solve for q 5.   q = 3p 6.   1/f = 1/p + 1/3p =4/3p   ;   solve for p 7.   p = 4*f/3 = 4*35/3 = 140/3 cm = 46.7 cm . 8.   4.5 = q/p   ;  solve for q 9.   q = 4.5p 10.   1/f = 1/p + 1/4.5p   =5.5/4.5p   ;   solve for p 11.   p = 5.5*f/4.5 = 192.5/4.5 cm = 42.8cm . 12.   Therefore, the object must be moved 3.9 cmcloser to the lens to increase the magnifiation from 3.0 to4.5. .

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