Question

A convex mirror has a focal length of -58.0 cm. A 12.0-cm-tall object is located 58.0 cm in front of this mirror. Determine the (a) location and (b) size of the image.

Answer 1

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A convex mirror has a focal length of -43.0 cm. A 12.0 cm tall object is located 45.0 cm in front of this mirror.
(a) Using a ray diagram drawn to scale, determine the location of the image. Note that the mirror must be drawn to scale.
cm

(b) Using a ray diagram drawn to scale, determine the size of the image. (Use a negative sign for an inverted image, positive for upright.)
cm

Focal length (f) of the convex mirror = - 43.0 cm
Height (h) of the object = 12.0 cm
Object distance (p) of the convex mirror = 45.0 cm
We know the mirror equation is
(1 / f) = (1 / p) + (1 / q)
(1 / q) = (1 / f) - (1 / p)
= (1 / -43.0cm) - (1 / 45.0cm)
q = -21.99 cm
q = -22.0 cm
Therefore the image is formed at a distance of 22.0 cm back to the mirror.
(b)
We know that magnification is
M = -q / p
= -(-22.0cm)/(45.0cm)
= 0.49
Then the height of the image is
h' = hM
= (12.0cm)(0.49)
= 5.88 cm