A 5.0 cm high object is situated 21.0 cm in front of a concave mirror that has a

Question

A 5.0 cm high object is situated 21.0 cm in front of a concave mirror that has a radius of curvature of 11.0 cm. Draw a ray diagram to scale. (Do this on paper. Your instructor may ask you to turn in the diagram.) Use the diagram to find the following answers. (a) the image distance (include the sign)
1      cm   2---Select---in front of the mirrorin back of the mirror     

(b) the height of the image
3      cm   4---Select---uprightinverted (a) the image distance (include the sign)
1      cm   2---Select---in front of the mirrorin back of the mirror     

(b) the height of the image
3      cm   4---Select---uprightinverted

Explanation / Answer

Let:
u be the object distance,
v be the image distance,
r be the radius of curvature,
f be the focal length,
m be the magnification,
H be the image height,
h be the object height.

The equations I use are:
1 / u + 1 / v = 2 / r = 1 / f
m = v / u
H = mh = vh / u
with f and r positive for a concave mirror, and negative for a convex mirror.

1.
1 / 21 + 1 / v = 2 / 11
1 / v = 2/ 11 - 1 / 21
v = 7.45 cm.

H = vh / u
= 7.45 * 5.0 / 21
= 1.77 cm.

That's an inverted, real image in front of the mirror.

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