In a darkened room, a burning candle is placed 1.65 m from a white wall. A lens

Question

In a darkened room, a burning candle is placed 1.65 m from a white wall. A lens is placed betweencandle and wall at a location that causes a larger, inverted imageto form on the wall. When the lens is moved 95.0 cm toward the wall, another image of the candleis formed. (a) Find the two object distances that producethe images just described.
p1 = m
p2 = m

(b) Find the focal length of the lens.
f = m

(c) Characterize the second image.
M2 =
Thus, the second image is ---Description---real, inverted, and diminished.virtual, inverted, and diminished.real, inverted, and enlarged.virtual, upright, and enlarged. PLEASE HELP!! (a) Find the two object distances that producethe images just described.
p1 = m
p2 = m

(b) Find the focal length of the lens.
f = m

(c) Characterize the second image.
M2 =
Thus, the second image is ---Description---real, inverted, and diminished.virtual, inverted, and diminished.real, inverted, and enlarged.virtual, upright, and enlarged. PLEASE HELP!!

Explanation / Answer

1 / f = 1 / o + 1 / i     or   f = o i / (i + o) Thus o1 i1 = o2i2    (I)     since the sum of the object & image distances is 1.65 m in bothcases o2 - o1 =.95       the mirror is moved .95 maway from the candle o1 i1 / i2 -o1 = .95      usingequation (I) o1 ( i1 - i2) / i2= .95 But i1 - i2 =.95      (II)   since thelens is moved .95 cm closer to the wall This gives o1 = i2 Since  o1 + i1 =1.65 i1 + i2 = 1.65   i1 - i2 =.95       eq (II) 2 i1 =2.6        and i1 =1.3 m Now you can easily get the otherdistances    Since f = 1.3 * .35 / 1.65 = .276 = 27.6 cm theobject is outside the focal length of the lens in both cases and a real inverted image is formed M = -i /o        themagnification       Since  o1 + i1 =1.65 i1 + i2 = 1.65   i1 - i2 =.95       eq (II) 2 i1 =2.6        and i1 =1.3 m Now you can easily get the otherdistances    Since f = 1.3 * .35 / 1.65 = .276 = 27.6 cm theobject is outside the focal length of the lens in both cases and a real inverted image is formed M = -i /o        themagnification      

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