Question
A student says: “If half of a convex lens is covered with opaque paper, only half the image will form.” Another student says: “The full image still forms but with reduced brightness.” Who is correct? Resolve this with the principle of how images are formed by a lens.
Solution — Step by Step
Every point on the object emits light in all directions. A lens collects rays from each object point and converges them to the corresponding image point. Each point of the lens contributes to every point of the image — not just to a specific region.
If you block half the lens, you stop half the rays from reaching the image plane. But the remaining half-lens still receives rays from the entire object and focuses each object point to the correct image point.
The full image still forms — only with reduced intensity (about half the brightness, since only half the light gets through). Student 2 is correct.
Why This Works
The image-forming property comes from the geometry of refraction at the lens surface, not from the location on the lens. Any small portion of a lens — even just a sliver — can form a complete image. This is why telescopes with central obstructions (like Cassegrain reflectors) still produce full images.
The half you cover doesn’t correspond to a particular half of the image. It corresponds to a particular set of rays through the lens. Removing those rays reduces brightness uniformly across the entire image.
Same principle for camera apertures: a smaller aperture (covering more of the lens) doesn’t crop the image — it reduces brightness and increases depth of field. This is the mechanism behind every aperture setting on a DSLR.
Alternative Method
Use the principal-ray construction. The principal axis ray, the ray through the optical centre, and the parallel ray are the three rays we draw — but the image actually forms from infinitely many rays between these. As long as some rays from each object point reach the focal plane, the image forms. Blocking half the lens removes some of these rays per object point, but not all.
Students think “half lens = half image” because that’s intuitive for shadows. Lens optics is not shadow geometry — it is convergence of rays. Each object point connects to the entire lens, not just one part.
Common Mistake
A related trap: students believe that if you cover the central portion of the lens, the image disappears. Wrong. The image still forms, just with reduced intensity. Try it with any magnifying glass at home — block the centre with a coin, and the image of a distant lamp still focuses on a wall.
Final answer: Student 2 is correct. The full image forms, with reduced brightness.