Points to Ponder

Reflection and refraction laws are universal. The laws of reflection and refraction apply at the point of incidence for any surface shape and any pair of media — they are not limited to flat surfaces or specific materials.

The real image exists even without a screen. When an object lies between $f$ and $2f$ from a convex lens, a real image forms at a specific location in space. Removing the screen does not destroy the image — the rays still converge to that point and then diverge. The screen merely diffuses these rays so our eyes can see them. This is why laser shows can project images in mid-air.

Image formation requires regular reflection/refraction. For a clear image, all rays from a single object point must converge to (or appear to diverge from) the same image point. This is why a rough surface like a book page cannot form your reflection — it scatters rays irregularly, so no single image point exists.

Thick lenses cause colour dispersion, and object colour depends on incident light. Thick lenses split white light into colours due to dispersion. The colours we perceive on objects depend on which wavelengths of the incident light they reflect. Under monochromatic light, an object may appear completely different from how it looks in white light.

Simple microscope magnification comes from closer placement. In a simple microscope, the angular size of the object equals the angular size of the image. Magnification occurs because the lens lets you place the tiny object much closer than 25 cm, making it subtend a larger angle. Without the microscope, you would have to keep the object at 25 cm, where it subtends a very small angle. …