An object 4.0 cm in height is placed 18.0 cm in front of a concave mirror with a

Question

An object 4.0 cm in height is placed 18.0 cm in front of a concave mirror with a focal length of 20.0 cm. What is the position of its image in relation to the mirror and what are its characteristics? a) 40.0 cm on the other side of mirror, real, 6.0 times bigger b)10.0 cm on the same side of mirror, real, 6.0 times bigger c)180.0 cm on the other side of mirror, virtual, 10.0 times bigger d) 10.0 cm on the other side of the mirror, virtual, 10.0 times bigger e)18.0 cm on the same side of mirror, virtual, 2.25 times bigger

Explanation / Answer

When object is between focal point and mirror the image is Virtual, Upright and Magnified (larger).

1/s + 1/s' = 1/f
m = y'/y = – s'/s
1/18 + 1/s' = 1/20
1/s' = 1/20 – 1/18 = (9 – 10) /180
s' = -180 = -180 cm
m = - s'/s = - (-180)/18 = 10
m = y'/y
y' = m y = 10 * 4 = 40 cm
Since s' < 0 => Virtual
Since m > 0 => Upright
Since m > 1 => Magnified

180cm on the other side of the mirror, virtual, 10 times bigger .

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