Position of image of an immersed object

In summary, the conversation discusses the position of the image of an immersed object and whether it is always vertically above the object regardless of the viewing position. It is pointed out that most books only show the case where the image is viewed from vertically above, which is related to using apparent depth of water to measure refractive index. However, there is another caustic curve that shows the change in position of the image when viewing from different angles. The diagram provided in the conversation illustrates this concept.
  • #1
nilic1
39
0
Position of image of an immersed object.. Are books wrong?

Homework Statement



In almost every book I checked, the image of an immersed object is always vertically above the object. Is this always the case and is independent on the position you are looking from?

Homework Equations



n = sin i / sin r

The Attempt at a Solution



According to my drawings the image is only VERTICALLY above the object if you look directly from above. I used snell's law to find the angles i and r, and then located the image. I always used 2 rays emerging from the object and was extra careful to mark the angles accurately and pass through the right positions. I also tried to find some flash or java animation that could illustrate this but I couldn't find any. Are the books wrong?
 
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  • #2
You are perfectly correct.
Most books show the case where the image is viewed from vertically above. It's usually in connection with using apparent depth of water to measure the refractive index.
The books should explain that this is the case, and only relates to a narrow bundle of rays moving vertically upwards.
There is a diagram here from one of my old books which shows how the position of the image changes as you view from a point further to the right.
The images are I1 I2 and I3 and lie on a curve called a "caustic". I1 is the standard case when viewed from vertically above.
There are two caustics in the diagram. There is also the one on the left for the case when you view from the left.
The diagram isn't perfectly clear but does show the point you have correctly brought up.
apparent-depth.png
 
  • #3
Many thanks, I looked everywhere for this diagram but couldn't find it anywhere neither in books nor on the net.
 

FAQ: Position of image of an immersed object

What is the position of the image of an immersed object?

The position of the image of an immersed object refers to the location of the image formed by the refraction of light as it passes through a medium, such as water or glass, and interacts with the object.

How is the position of the image of an immersed object determined?

The position of the image of an immersed object is determined by the laws of refraction, specifically Snell's law, which describes the relationship between the angles of incidence and refraction as light passes through a medium.

Can the position of the image of an immersed object be predicted?

Yes, the position of the image of an immersed object can be predicted using the laws of refraction and the properties of the medium through which the light is passing. It can also be calculated using mathematical equations and diagrams.

What factors affect the position of the image of an immersed object?

The position of the image of an immersed object is affected by the properties of the medium, such as its refractive index, as well as the shape, size, and position of the object itself. The angle of incidence and the angle of refraction also play a role in determining the position of the image.

Why is understanding the position of the image of an immersed object important?

Understanding the position of the image of an immersed object is important in various fields, such as optics, engineering, and biology. It allows scientists to predict and manipulate the behavior of light in different mediums, which has practical applications in areas such as lens design, underwater imaging, and medical imaging.

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