Calculating Apparent Depth Using Snell's Law

In summary, the problem involves determining the apparent depth of a fish viewed from above the water surface using Snell's law. The angle of refraction in water is found to be approximately 48.75 degrees when the angle of incidence is set to 90 degrees. To find the apparent depth, we can use right triangles in the diagram to calculate the difference between the real depth and the apparent depth. The correct answer is 60 cm.
  • #1
roam
1,271
12

Homework Statement



A fish is 80 cm below the surface of a pond. What is the apparent depth (in cm) when viewed from a position almost directly above the fish? (For water, n = 1.33.)

Homework Equations



Snell's law: [tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]

The Attempt at a Solution



So far I have found the angle of refraction in the water using Snell's law. Since they are asking for "a position almost directly above the fish", I took [tex]\theta_1 = 90[/tex].

[tex]1= 1.33 sin \theta_2[/tex]

[tex]\theta_2 = 48.75[/tex]

But I what else can I do?? I'm really stuck! I need to find the difference between he apparent and the real depth x, 80-x=apparent length. But how? Here's a diagram which shows a similar situation:

phys.gif


The correct answer is 60 cm.
 
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  • #2
The angle in Snell's law is measured from the normal of the water surface, and it is near zero now.

ehild
 
  • #3
ehild said:
The angle in Snell's law is measured from the normal of the water surface, and it is near zero now.

ehild

If this angle is zero, then what do I need to do to find the apparent depth?
 
  • #4
It is not zero, just small.

ehild
 
  • #5
Oh, okay. How does this help us to determine the apparent depth?
 
  • #6
Look at the figure and find some right triangles.

ehild
 

1. What is Apparent Depth?

Apparent depth is the perceived depth of an object when viewed from a different medium, such as water or air. It is different from the actual depth of the object.

2. What is Snell's Law?

Snell's Law, also known as the Law of Refraction, is a principle that describes how light bends when it passes through different mediums, such as from air to water. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums.

3. How does Apparent Depth relate to Snell's Law?

Apparent depth is affected by Snell's Law because as light travels from one medium to another, it bends according to the law. This change in direction of light causes the apparent depth of an object to appear different from its actual depth.

4. What is the relationship between the angle of incidence and the angle of refraction in Snell's Law?

The angle of incidence and the angle of refraction are related by Snell's Law. The angle of incidence is the angle at which light enters a medium, while the angle of refraction is the angle at which light bends as it passes through the medium. According to Snell's Law, the sine of the angle of incidence divided by the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums.

5. How is Snell's Law used in everyday applications?

Snell's Law is used in various everyday applications, such as eyeglasses, cameras, and microscopes. It is also used in the design of lenses and prisms. Additionally, it is important in understanding the behavior of light in different mediums, which has implications in fields such as optics, astronomy, and oceanography.

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