Physics

Problem

An object is placed

18\,\text{cm}

in front of a concave mirror of focal length

-12\,\text{cm}

. A student calculates the image distance as

v=+36\,\text{cm}

and concludes that the image is virtual and located behind the mirror. Which option best explains why this conclusion shows a sign-convention mistake? a) The error comes from treating the concave mirror’s focal length as positive; if

f=+12\,\text{cm}

is used, one obtains

v=+7.2\,\text{cm}

, a virtual image b) There is actually no sign mistake: any positive value of

v

simply means the image is real, so the student’s conclusion is acceptable c) The correct calculation gives

v=-36\,\text{cm}

; the negative sign indicates a real image in front of the mirror, so taking

v

as positive is the mistake d) The student should have taken the object distance as

+18\,\text{cm}

; doing so gives

v=-7.2\,\text{cm}

and removes the sign conflict

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