OPTICS OBJECTIVE 7

Problem 7: Brightness Distribution in Image

Analysis

1. Image Orientation: The object is placed at $1.25f$, which forms a Real and Inverted image.
   • The “Upper half of the image” (points near the axis) corresponds to the “Lower half of the object” (base of the arrow).
   • The “Lower half of the image” (points far below the axis) corresponds to the “Upper half of the object” (tip of the arrow).
2. Light Path Analysis:
   • Upper Object (Tip): Rays from the tip of the object travel towards the lens. Due to the geometry and directionality of the emitted cone of light, a significant portion of these rays are directed towards the upper half of the lens. Since the upper half is covered, most of the light contributing to the image of the tip is blocked.
   • Lower Object (Base): Rays from the base (on the principal axis) are distributed symmetrically over the lens. Blocking the upper half removes exactly 50% of the light, but the remaining 50% passes through the lower half to form the image.
3. Result:
   • The image of the Tip (Lower half of image) receives significantly less light (is much dimmer).
   • The image of the Base (Upper half of image) receives relatively more light (is brighter).