A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, then :

Question

Accepted Answer

When a convex lens forms a real image of a point object placed on its principal axis, the entire lens is involved in focusing the light rays to form the image. If the upper half of the lens is painted black, the lens still retains its ability to focus light, but only through the unpainted lower half. Here's why Option 3 is correct and the other options are incorrect:

1. **Explanation for Option 3 (Correct Answer):**  
   The image will not be shifted. When the upper half of the lens is painted black, the lens still functions as a convex lens, but with reduced aperture. The light rays from the object that pass through the lower half of the lens will still converge at the same point on the principal axis to form the image. The position of the image is determined by the lens formula and the geometry of the lens, which remains unchanged. Therefore, the image will not shift from its original position.

2. **Why Option 1 is Incorrect:**  
   The image will not be shifted downwards. The position of the image is determined by the focal length of the lens and the object distance, which are not affected by painting half of the lens. The rays that pass through the lower half will still converge at the same point on the principal axis, so there is no downward shift.

3. **Why Option 2 is Incorrect:**  
   The image will not be shifted upwards. Similar to the reasoning for Option 1, the convergence point of the rays remains on the principal axis. The painting of the upper half does not alter the focal properties of the lens, so there is no upward shift.

4. **Why Option 4 is Incorrect:**  
   The intensity of the image will change. Painting the upper half of the lens reduces the amount of light passing through the lens, as only the lower half is now contributing to the image formation. This reduction in light results in a decrease in the intensity or brightness of the image, contrary to what Option 4 suggests.

In summary, painting the upper half of the lens does not affect the position of the image, which is why Option 3 is the correct answer. The image remains at the same location on the principal axis, although its intensity is reduced due to the decreased aperture size.