Compare the shadows cast by a pole in the river and a pole on the shore

In summary, the conversation discusses the difference in the length of shadows when light travels through water compared to land due to the slower speed of light in water. It also mentions how a ray of light grazing the top of a pole would deflect close to the normal line, resulting in a shorter shadow in water.
  • #1
hidemi
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Homework Statement
A pole stands in a river, half in and half out of the water. Another pole of the same length stands vertically on the shore at a place where the ground is level. The shadow cast by the pole in the river on the river bottom is:

A. slightly longer than the shadow of the pole on land
B. much longer than the shadow of the pole on land
C. shorter than the shadow of the pole on land
D. shorter than the shadow of the pole on land if the Sun is high and longer if the sun is low
E. the same length as the shadow of the pole on land

The answer is C
Relevant Equations
v=f*λ
Is it because the speed of light is less fast in the water than on land as such leads to different in length of shadow?
 
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  • #2
hidemi said:
Is it because the speed of light is less fast in the water than on land as such leads to different in length of shadow?
Only indirectly.

If you traced a ray of light from the source to the tip of the pole and then straight past that until it strikes the river bottom, that would be the edge of the shadow, right?

What happens to that light ray when it strikes the surface of the river water?
 
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  • #3
In a way yes. Consider the ray that just grazes the top of the pole. Draw a ray diagram for each of the two cases.
 
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  • #4
jbriggs444 said:
What happens to that light ray when it strikes the surface of the river water?
The ray of light would deflect close to the normal line which makes the shadow less longer in the water.

Thanks both of you!
 
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FAQ: Compare the shadows cast by a pole in the river and a pole on the shore

What causes the differences in the shadows cast by a pole in the river and a pole on the shore?

The differences in the shadows are caused by the reflection and refraction of light. When the pole is in the river, the light from the sun is reflected off the surface of the water, causing the shadow to appear distorted and elongated. On the shore, the light is only affected by the pole itself, resulting in a more defined and accurate shadow.

Why does the shadow of the pole in the river appear longer than the shadow of the pole on the shore?

The shadow of the pole in the river appears longer because of the angle of incidence. When the light hits the surface of the water, it is refracted and bent, making the shadow appear longer than it actually is. On the shore, the light hits the pole at a more direct angle, resulting in a shorter shadow.

Do the shadows of the pole in the river and the pole on the shore change throughout the day?

Yes, the shadows will change throughout the day as the position of the sun in the sky changes. This will affect the angle of incidence and the length and direction of the shadows.

How does the depth of the water in the river affect the shadows of the pole?

The depth of the water in the river can affect the shadows of the pole by changing the angle of reflection and refraction. If the water is shallow, the light will not be able to penetrate as far, resulting in a shorter shadow. If the water is deeper, the light will be able to travel further, resulting in a longer shadow.

Is there a difference in the shadows of the pole in a still river versus a moving river?

Yes, there can be a difference in the shadows of the pole in a still river versus a moving river. In a still river, the reflection and refraction of light will be more consistent, resulting in a more consistent shadow. In a moving river, the movement of the water can cause the light to be refracted and reflected in different directions, resulting in a more distorted shadow.

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