Question

One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answers experimentally? Explain your observations.

Answer 1

Hint: If the top half portion of the convex lens is covered, we are actually blocking half of the coming rays incident on the lens. We will perform an experiment with the help of a convex lens, a lighted candle and a sheet of paper to determine whether a half-covered convex lens can produce a complete image of the object.

Complete step-by-step answer:
A single point on the object needs only two rays passing from the lens to form an image. Since the entire convex lens is not covered, at least two rays from each point on the object can pass through the lens, and hence, the image will be formed. However, since the number of rays involved in the image formation has reduced as the lens is covered, the image formed is less intense and less bright.
Experiment: To verify whether a half-covered convex lens can produce a complete image of the object.
Apparatus needed: A Convex lens, a candle, and two black sheets of paper.
Procedure:
1. Mount a convex lens on the table. Light a candle with a match stick and place it near one side of the lens on the table. Turn off the lights of the room in order to get dark.
2. Take the sheet of paper and place it on the other side of the lens as the candle.
3. Now focus the image formed on the sheet of paper by moving the sheet only.
4. Observe the image carefully.
5. Mark the positions of candle, lens and screen.
6. Now, turn off the light. Take the convex lens and cover half of it with the second sheet of black paper.
7. Mount the lens on the table in the original position and repeat the above experiment.

Observations:
A focused image of the object, or the candle, is obtained in both the experiments. However, the image formed with half of the convex lens covered is less bright as compared to when the lens is uncovered.

Conclusion:
If the top half portion of the lens is covered, we are blocking half the rays incident on it. Image will be formed by the rays of the bottom half of the lens. This means that every broken piece of the lens which has a part of both the curved surface should be able to form an image, although a less bright image.

Note: Even if half of the convex lens is covered with a black sheet of paper, the lens will produce a complete image of the object. However, the intensity of the image will be less and the image formed will be less bright as compared to the one formed by a complete convex lens. The shape of the lens is irrelevant for an image to form. Also, the shape of the lens does not show in the image of the object or manipulate the image in any way other than the brightness provided it has a part of two curved surfaces in line.