A 4.0-cm-tall candle flame is 2.0 m from a wall. Y...

Question

A 4.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 42cm.

A) How many places can you put the lens to form a well-focused image of the candle flame on the wall? Answer: 2

B) What are the distance between the candle and the lens for each location? Answer: 60 and 140 cm

C) For each location, what is the height of the image?

Patrick Ford · Accepted Answer

Lens equation:1so+1si=1f[readmore]A)We are given:Object height, hi = 4.0 cmSum of object and image distance, so + si = 2.0 m = 200 cmFocal length, f = 42 cmNow we have:142=1so+1200-soso2-200so+8400=0This is a quadratic expression.Since we have a quadratic expression, we'll have two possible positions to put the lens. The number of places you can put the lens to form a well-focused image of the candle flame on the wall is 2.B)We'll use the quadratic formula:x=-b±b2-4ac2a, where:x = soa = 1b = - 200c = 8400Substituting:so=-(-200)±(-200)2-(4)(1)(8400)(2)(1)=200±802so = 140 cm or 60 cmThe distance between the candle and the lens for each location is 140 cm and 60 cm.C)Magnification:m=hiho=-sisoFrom magnification:hiho=-sisohi=(-siso)hoAt the position, 60 cm:si = 200 - 60 = 140 cmhi=(-14060)(4)hi = - 9.3 cmWhen the object is placed at position 140 cm, si = 200 - 140 = 60 cmhi=(-60140)(4)hi = - 1.71 cmThe heights of the image for positions 60cm and 140cm are - 9.3 cm and - 1.71 cm, respectively.

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