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Depth of a well is 5.5 m and the refractive index of water is 1.33. If viewed normally from the top, by how much height would the bottom of the well appear to be shifted up?

Asked in GSEB Board July 2015; GSEB Board March 2020 (old course) · Snell's law, slabs and apparent depth

• (1) 5.5 m
• (2) 2.75 m
• (3) 4.13 m
• (4) 1.37 m

Step-by-step solution

Why the other options are wrong

• (1) comes from the full depth of the well, not the shift. Water lifts the bottom only part of the way; it cannot bring it to the surface.
• (2) comes from half the depth, which would need n=2: d(1-1/n)=d/2 only when 1/n=1/2. For water n=1.33 and the shift is about a quarter of the depth.
• (3) (5.5)/(1.33)=4.13 m is the apparent depth itself, the answer to a different question. The shift is what is left over, 5.5-4.13.

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