Position of image of an immersed object

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SUMMARY

The discussion clarifies that the position of the image of an immersed object is not always vertically above the object, as commonly depicted in textbooks. This vertical alignment occurs only when viewed directly from above, as demonstrated using Snell's Law (n = sin i / sin r) to calculate angles. The images formed by rays diverging from the object lie on a curve known as a "caustic," which varies based on the viewer's position. The discussion emphasizes the need for textbooks to specify these conditions to avoid misconceptions.

PREREQUISITES
  • Understanding of Snell's Law (n = sin i / sin r)
  • Basic knowledge of optics and light refraction
  • Familiarity with ray diagrams and image formation
  • Concept of caustics in optics
NEXT STEPS
  • Research the concept of caustics in optics and their mathematical representation
  • Explore advanced applications of Snell's Law in different mediums
  • Investigate software tools for simulating light refraction and ray tracing
  • Study the apparent depth of water and its relation to refractive index measurements
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Students of physics, educators teaching optics, and anyone interested in the principles of light refraction and image formation in different media.

nilic1
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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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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
 
Many thanks, I looked everywhere for this diagram but couldn't find it anywhere neither in books nor on the net.
 

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