The correct option is (c).
Explanation
The apparent movement of celestial bodies, including the Sun, across the sky is primarily determined by the Earth's rotation on its axis. The length of shadows cast by objects on Earth depends on the angle of elevation of the Sun relative to the horizon.
Statement-wise Analysis:
- Statement 1 is Correct: The Earth rotates on its axis from West to East (counter-clockwise when viewed from above the North Pole). This prograde rotation is the fundamental reason for the apparent diurnal motion of the Sun, Moon, and stars.
- Statement 2 is Incorrect: As a direct consequence of the Earth rotating from West to East, the Sun appears to move in the opposite direction. Therefore, the Sun appears to rise in the East and set in the West.
- Statement 3 is Correct: The length of a shadow is inversely proportional to the angle of the Sun's elevation. At noon (specifically local apparent noon), the Sun reaches its highest point in the sky (zenith or meridian transit). Because the light rays hit the object from the steepest angle possible for that day, the shadow cast is at its shortest length. Conversely, shadows are longest at sunrise and sunset when the Sun is near the horizon.
Key Takeaway:
The Earth rotates from West to East, causing the Sun to rise in the East. Shadow length is determined by the Sun's altitude; it is shortest at local noon when the Sun is at its peak altitude.