In geometrical optics, what type of lens is used in a simple magnifying glass to enlarge the apparent size of objects?

Introduction / Context:
A magnifying glass is a common optical device used to view small objects with an apparently larger size. At a basic physics level, it consists of a simple lens that produces a magnified virtual image when the object is placed within its focal length. This question asks you to identify which type of lens is used in a magnifying glass in terms of its converging or diverging nature.

Given Data / Assumptions:
- The device is a simple hand-held magnifying glass used for everyday magnification.
- Options include diverging lens, spherical mirror, converging lens and a more specialised achromatic lens.
- We assume simple single-lens magnifiers, not advanced microscope objectives.

Concept / Approach:
A magnifying glass uses a convex (converging) lens with positive focal length. When an object is placed between the lens and its focal point, the lens forms a virtual, erect and magnified image on the same side of the lens as the object. Diverging lenses, such as concave lenses, cannot be used alone to obtain a magnified upright virtual image in this way for a nearby object. Spherical mirrors are different devices entirely, and achromatic lenses are more advanced designs used to reduce chromatic aberration, not essential for a simple magnifying glass concept.

Step-by-Step Solution:
Step 1: Recall that a standard magnifying glass is typically a convex lens, which is a converging lens. Step 2: When you place an object within the focal length of this lens, it forms a virtual, enlarged and upright image. Step 3: Diverging lenses (concave lenses) cause rays to spread out and usually produce smaller virtual images, not the magnified images desired in a simple magnifier. Step 4: A spherical mirror is a different optical element, not what we mean by a magnifying glass lens. Step 5: Achromatic lenses are combinations of lenses designed to correct for colour dispersion, and while some magnifiers may use them, the basic conceptual answer is still that a magnifying glass uses a converging lens. Step 6: Therefore, the correct type of lens is a converging lens.

Verification / Alternative check:
Ray diagrams from textbook optics show that a convex lens can produce a magnified virtual image if the object is inside the focal length, making it ideal for magnifying glasses. Many simple optical instruments, including magnifiers and some microscopes, use converging lenses in this configuration. On the other hand, concave lenses are used to correct myopia and to enlarge fields of view but do not serve as basic magnifying glasses for nearby objects.

Why Other Options Are Wrong:
Diverging lens: A diverging lens alone usually produces a diminished virtual image and therefore is unsuitable as a simple magnifying glass.
Spherical mirror: Mirrors reflect light rather than refract it; they are not what is meant by the lens in a magnifying glass.
Achromatic doublet only: While an achromatic doublet may be composed of converging and diverging elements to reduce chromatic aberration, the core magnifying effect still comes from converging lens behaviour; the question is about basic type, not specialised corrected designs.

Common Pitfalls:
Some learners confuse convex and concave lenses because both are curved and may appear similar at a glance. Remember that a simple magnifying glass is thicker in the middle than at the edges, which is characteristic of a convex (converging) lens. Drawing ray diagrams for both types of lenses with an object placed inside focal length is a good way to cement the correct concept in your mind.

Final Answer:
A magnifying glass uses a converging lens, typically a convex lens, to enlarge the apparent size of objects.