(a) The height of the image is 1.5 cm.
(b) The warning is due to convex mirror's ability to diverge light rays, making objects appear smaller and farther away than they actually are.
How to calculate the image distance?
The image distance is calculated by applying the following formula as follows;
-1/f = 1/u + 1/v
where;
- f is the focal length
- u is the object distance = 9m = 900 cm
- v is the image distance = ?
The focal length = r/2
f = 18 cm / 2
f = 9 cm
-1/9 = 1/900 + 1/v
1/v = -1/9 - 1/900
1/v = -0.1122
v = 1/(-0.1122)
v = -8.9 cm
(a) The height of the image is calculated as;
M = Hi/h = v/u
Hi/1.5 = 8.9 / 900
Hi = 1.5 x (8.9/900)
Hi = 0.015 m
Hi = 1.5 cm
(b) The warning on the mirror ("objects are closer than they appear") is due to the convex mirror's ability to provide a wider field of view. Convex mirrors diverge light rays, making objects appear smaller and farther away than they actually are.