A spherical convex mirror has a radius of curvature of magnitude of 20cm. At what distance from the mirror should an object be placed to obtain an image that is virtual, four times smaller and upright.

To find the distance of the object from the convex mirror, we can use the mirror equation, which is:

1/f = 1/v - 1/u

Where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror (positive for virtual images)
- u is the distance of the object from the mirror (positive if the object is in front of the mirror)

In this case, we know that the image formed is virtual, four times smaller, and upright.

Given the radius of curvature (R) of the mirror, we can deduce that the focal length (f) is half the magnitude of the radius, which is 20 cm/2 = 10 cm.

Since the image is four times smaller, the magnification (m) is 1/4. The magnification can be calculated as:

m = -v/u

Since the image is upright, the magnification is negative.

Substituting the values into the magnification equation, we have:

1/4 = v/u

Solving for v in terms of u, we get:

v = u/4

Now, substituting the values into the mirror equation, we have:

1/10 = u/4 - 1/u

Multiplying through by 40u, we get:

4u = 10u - 40

Rearranging the equation, we have:

6u = 40

Dividing both sides by 6, we get:

u = 40/6 = 6.67 cm

Therefore, the object should be placed at a distance of approximately 6.67 cm from the convex mirror to obtain a virtual, four times smaller, and upright image.