Apparent Depth at Normal Viewing
For a plane interface, small angles and an observer in medium n1 viewing an object in medium n2, apparent depth/real depth = n1/n2.
Why this shows up in the exam
Depth gauges · Microscope focusing through liquid · Apparent-rise measurements
Learn the idea
A submerged object viewed nearly normally appears shallower because refracted rays seem to come from above it. The eye extends emerging rays backward in straight lines and locates a virtual image closer to the interface.
🧠 Memory hook: From air into water, divide real depth by the relative index.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- d_app/d_real = n_observer/n_object — paraxial viewing through one plane interface
- shift = d_real - d_app — apparent upward shift for viewing from the lower-index side
How to approach it
- 1Identify observer and object media
- 2Check the paraxial condition
- 3Compute each apparent thickness in the observer's medium
Common slip-ups that cost marks
- •Applying the formula at large viewing angles
- •Using total vessel depth instead of layer depth
- •Reversing observer and object indices
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A real object is placed 30 cm from a converging lens of focal length 10 cm. Find the real image distance.
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