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Does the viewing angle of a person observing a coin placed in a bucket of water affect the apparent depth in any way?

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  • $\begingroup$ This question appears to be off-topic because it is obvious. $\endgroup$ – Abhimanyu Pallavi Sudhir Feb 16 '14 at 15:17
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    $\begingroup$ How is it obvious? $\endgroup$ – BMS Feb 16 '14 at 15:29
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    $\begingroup$ @Artemisia One thing you might want to try is drawing a very careful diagram showing light leaving an object under water at different angles. You'd need a protractor & such to get the angles just right. Trace back your rays and see if you're able to say either way. $\endgroup$ – BMS Feb 16 '14 at 15:32
  • $\begingroup$ That helped provide the intuition to support the derivation given below :) Thank you $\endgroup$ – Artemisia Feb 16 '14 at 17:26
  • $\begingroup$ Related and useful : How does apparent depth depend on viewing angle? $\endgroup$ – user14250 Dec 28 '19 at 13:37
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Apparent depth of the object is given by the following equation,
$$AD=\frac{RD}{n_{ab}}$$
Where $AD$ is apparent depth, $RD$ is real depth, and $n_{ab}$ is the refractive index of medium b (denser medium) w.r.t medium a (rarer medium).

As real depth and refractive index is going to be constant always (for the given pair of medium), apparent depth will be independent of viewing angle.

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    $\begingroup$ The equation you give is only true when you're looking directly downwards, not at an angle, so I'm afraid you've drawn the wrong conclusion. $\endgroup$ – John Rennie Feb 16 '14 at 15:45
  • $\begingroup$ @JohnRennie. Thank you for the comment. Even when we look at an angle, refracted ray and incident ray will be such that refractive index will remain constant. So, I think apparent depth is not going to vary. If anything wrong here, I will be happy to know. $\endgroup$ – Immortal Player Feb 16 '14 at 15:51
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    $\begingroup$ When viewing at an angle, the image will be shifted both vertically and horizontally. I remember doing a problem in Irodov about it. $\endgroup$ – evil999man Apr 26 '14 at 12:21

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