Using the mirror formula, 1/f = 1/v + 1/u; here, v = -15 cm (real image) and u = -30 cm. Thus, 1/f = 1/(-15) + 1/(-30) = -1/10, so f = 10 cm.

Using the lens formula, 1/f = 1/v - 1/u. Here, v = -20 cm (virtual image), u = -10 cm. Solving gives f = 5 cm.

Magnification (m) = -v/u = -(-5)/(-15) = 1/3. Therefore, the magnification is 3.

A concave lens always produces a virtual and upright image regardless of the object's position.

A concave lens always forms a virtual and upright image.

When an object is placed beyond the focal length of a convex lens, the image formed is real and inverted.

When the object is at 2f, the image is formed at 2f on the opposite side, making it real and inverted.

When the object is at infinity, the rays converge at the focal point, forming a real and inverted image.

A convex mirror always forms a virtual image that is upright and smaller than the object.

When the object is placed between the focal point and the mirror, the image formed is virtual and upright.

A convex mirror always forms a virtual and upright image regardless of the object's position.

A convex lens can produce both real images (when the object is outside the focal length) and virtual images (when the object is within the focal length).

A convex lens can produce both real images (when the object is outside the focal length) and virtual images (when the object is within the focal length).