Geometrical optics. Photometry. Quantum nature of light > Photometry > Problem 13.4.11

Statement

What happens to the image given by the lens if the upper half of the lens is
painted over with black paint?

Solution

An image of the entire object will be produced albeit with reduced intensity. The intensity of the image of the middle part of the object will be reduced by exactly a half. The upper part of the object is closer to the upper part of the lens (which is painted black) and the intensity of its image will be reduced by more than a half. On the other hand, the lower part of the object is farther from the upper part of the lens, and the intensity of its image will be reduced by less than a half. (In the figure, light rays from each part of the object are evenly distributed.)

Answer

See the solution.