Question

A circular disc and a sphere of the same diameter are floating above the ground. The circular disc is parallel to the ground. Which option shows the CORRECT set of shadows on the ground when seen from the top? 

• A. A
• B. B
• C. C
• D. D

Hint:

When dealing with shadows, consider the angle of light. For flat objects like discs, shadows remain circular, while spherical objects cast elliptical shadows if the light is angled.

Answer 1

The Correct Option is A

Step 1: The shadow of a circular disc, when viewed from the top, will always be a circle because the disc is parallel to the ground.
Step 2: The shadow of the sphere will be elliptical due to the 45° angle of the sunlight. Since the sunlight is not directly above, the sphere’s circular shadow becomes elongated.
Step 3: Option (A) is the correct representation of a circular shadow for the disc and an elliptical shadow for the sphere.

Answer 2

The disc lies flat and parallel to the ground, while the sphere is a solid ball, and the sunlight arrives as parallel rays at a slant (45 degrees to the ground). Since the disc's own plane is already parallel to the ground, sliding it straight down along the direction of the sunlight to the ground does not stretch or squash its outline at all, so its shadow is a plain circle, the same size and shape as the disc itself. The sphere is different: the edge of its shadow comes from the circle of points on the sphere where the sunlight grazes past it, and that circle's plane is tilted relative to the ground because the light comes in at an angle, not straight down. Projecting a tilted circle onto the ground at a slant stretches it out into an ellipse, so the sphere's shadow is a wider oval, not a plain circle.

1. Option A: This pairs a plain circle for the disc's shadow with a wider oval for the sphere's shadow, matching exactly what the flat, parallel disc and the slanted grazing circle on the sphere should each produce.
2. Option B: Both shadows are shown as ovals here, but the disc's shadow should stay a plain circle, since the disc is already parallel to the ground and slanted light cannot stretch a shape that is not tilted relative to the surface it is being projected onto.
3. Option C: Both shadows are shown as circles here, but the sphere's shadow should be stretched into an ellipse because the grazing circle that forms its outline is tilted with respect to the ground under slanted sunlight.
4. Option D: The shapes are swapped here, an oval for the disc and a circle for the sphere, which is the reverse of what parallel projection under slanted light actually produces for a flat parallel disc and a sphere.

Only option A gives the disc a true circular shadow and the sphere a stretched, elliptical shadow, exactly as slanted parallel light on these two shapes should produce.

So the correct answer is Option A.