As scientists learnt more about how lenses worked, they were able to create better and better ones. By today's standards, even a simple magnifying glass is better made than some of the first optical instruments.
The very first scientific instrument that was built using lenses was the optical microscope. The simple microscope was made using just a single lens. This suffered from the problem that it could not provide high magnifications. Then someone came up with the idea of using two lenses so that the first magnified the image and the second then magnified that image, providing a much higher magnification than was possible with a single lens. This type of microscope is called a compound microscope - the microscopes you have used at school are of this type.
To focus the object under study, the microscope stage is moved closer to or further from the lenses. The lens closest to the object being observed is called the objective lens. The lens closest to the eye is called the eyepiece. In order to overcome lens defects, the objective lens and the eyepieces are themselves made up from several lenses. No one is certain who invented the first compound microscope, there are several possibilities but what is certain is that they were invented around the end of the sixteenth century. The first of these instruments to be called a microscope was the one made by Gallileo Gallilei; a colleague of Gallileo invented the name from the Greek words for 'small' and 'to look at'.
Another scientific instrument using lenses was invented at about the same time as the microscope - the telescope. Its development is credited to the same group of Dutch spectacle makers involved with the development of the microscope. When he heard about the telescope, Gallileo built himself one and became the first person to turn it toward the skies. He observed that Jupiter had several moons and even saw the rings around Saturn, but not very clearly. As with the microscope, the lens closest to the object being observed is the objective and the ones nearest to the eye make up the eyepiece. All of these early instruments had problems of chromatic aberration (light splitting into its component colours as it is refracted) and spherical aberration (light rays not all being focussed at exactly the same point) so the images would not have been very clear. Since the object being observed through a telescope is a long way away, it is the eyepiece that has to be moved to bring it into focus.
Concave and convex and only two type of lenses - there are many more, for example, meniscus lenses and plano-convex lenses. For the GCSE, you should be able to name types of lenses and also understand how each lens manipulates light rays passing through it. To do that, you need to be able to draw and interpret ray diagrams. You also need to know certain scientific terms associated with lenses and images.
When drawing ray diagrams for lenses, there are actually only two that you need to draw. Firstly, a ray that goes from the top of the object, passing through the exact centre point of the lens. This is drawn as a perfectly straight line. The other ray you need to draw is one that goes parallel to the axis of the lens, also from the top of the object. As it passes through the lens, this ray is bent and passes through the focal point of the lens, on the opposite side to the object.
If the rays converge (come together and meet) on the opposite side of the lens to the object, the image will be real (can be seen on a screen) and inverted (upside-down compared to the object).
If the rays of light diverge (get further apart and never meet) on the side of the lens opposite to the object, the image will be virtual and the right way up. On your diagram, you would use dotted lines to show this.