Chapter 27, Problem 42A

To determine

The reason that a high-flying plane cast little or no shadow on the ground, while a low-flying plane casts a sharp shadow.

Answer to Problem 42A

A total shadow is called umbra and a partial shadow is called penumbra. A penumbra appears when some of light is blocked but where other light fills in. When the height of the plane is large the more amount of sunlight (which is not a point source) fills in hence cast little or no shadow. On the other hand, for low-flying plane, there is not enough light to fill in hence do not blur and casts a sharp shadow.

Explanation of Solution

Introduction:

A shadow is formed where light rays cannot reach. Sharp shadows are produced by a small light source nearby or by a larger source farther away. However, most of the shadows are somewhat blurry.

There is usually a dark part on the inside of a shadow and lighter part around the edges of a shadow. A total shadow is called umbra and a partial shadow is called penumbra. A penumbra appears when some of light is blocked but where other light fills in as shown in following figure;

  

When the height of the plane is large the more amount of sunlight (which is not a point source) fills in hence cast little or no shadow. On the other hand, for low-flying plane, there is not enough light to fill in hence do not blur and casts a sharp shadow.

Conclusion:

Thus, a high-flying plane cast little or no shadow on the ground, while a low-flying plane casts a sharp shadow.