(a) Why magnification is taken negative for real images and positive for virtual images?
(b) Why convex mirror is used in rear view mirrors and not concave mirror?
Answers
Answer:
As per the new Cartesian convention, distances above the optical axis are taken as positive and distances below the optical axis are taken as negative.
Magnification is the ratio of the height of the image to the height of the object.
In case of a real image, the image is inverted and hence the height of the image has a negative sign, while the height of the object has a positive sign.
⇒⇒ The magnification negative.
In case of a virtual image, the image is erect and hence the height of the image has a positive sign. The height of the object also has a positive sign.
⇒⇒ The magnification positive.
If concave mirrors are used a rear view mirrors in vehicles instead of convex mirrors, the images of the objects beyond the focal length would be inverted. We are not used to seeing inverted images.
Further, the nearer objects, between the focal length and twice the focal length, would be magnified. This would make it very difficult for us to see clearly the objects that are farther away.
Convex mirrors always produce images that are virtual, upright and diminished.
Explanation:
According to the spherical mirror equation,
1
u
+
1
v
=
2
R
,
Since
u
is positive and
R
is negative,
v
will always be negative, and smaller in magnitude than
u
. Therefore the image will always be upright (not upside-down), virtual and diminished.
In the case of concave mirror, images of objects further from the focal point (
R
2
from the mirror) will be inverted, which is no good to a driver. For objects nearer than the focal point, the image would be magnified. Given the small area of the rear, less images can fit in it. But more importantly, near objects may not be of little interest to drivers, and concave mirrors are not suitable to view far objects.
For convex mirrors, diminished images means that images appears smaller than the objects, which means that a larger field of vision could be obtained. This is also why a convex mirror is preferred over a planar one.
In summary, the driver needs a wide view of the road situation that are (relatively) far away, and convex mirrors are able to acheive that.