Complex apparent and real depth problemm

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    Complex Depth
AI Thread Summary
The problem involves calculating the apparent depth of a logo embedded in a block of transparent material when viewed from above the water's surface. The initial depth of the logo is 3.59 cm in a block with a refractive index of 1.73, and there is an additional 1.86 cm of water above it. The equation for apparent depth is applied first for the transition from glass to water, and then from water to air. The calculations yield an apparent depth of 4.162 cm, but clarification is needed on how to find the final apparent location below the water surface. The discussion emphasizes the importance of correctly applying the equations for each medium transition to achieve the desired result.
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Homework Statement



A small logo is embedded in a thick block of transparent material (n = 1.73), 3.59 cm beneath the top surface of the block. The block is put under water (n = 1.333), so there is 1.86 cm of water above the top surface of the block. The logo is viewed from directly above by an observer in air. How far beneath the top surface of the water does the logo appear to be?


Homework Equations



apparent depth = dn_2/(n_1)

The Attempt at a Solution



What i tried doing is applying this equation twice. First with glass and water 3.59(1.33/1.73). Then with water and air 1.86(1/1.33). After that I added the two values of the apparent distances which I got 4.162
 
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pistonsfan321 said:
What i tried doing is applying this equation twice. First with glass and water 3.59(1.33/1.73).
OK. That's the apparent location of the first image below the block surface. What's the location of that image below the water surface? That's the distance you want when using the equation the second time.
 
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