Travelling Microscope and Apparent Depth
For near-normal viewing through a plane slab, refractive index is real depth divided by apparent depth; the required depths are differences of corrected travelling-microscope readings, each resolved by its vernier least count.
Why this shows up in the exam
Glass-slab refractive index · Liquid apparent-depth measurement · Small vertical displacement measurement
Learn the idea
A travelling microscope measures vertical focus shifts, letting apparent depth determine refractive index. Refraction makes a viewed mark appear raised. Focusing successively on reference surfaces turns that optical shift into scale differences, while the attached vernier sets the reading resolution.
🧠 Memory hook: Refraction raises the image, so apparent depth is smaller.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- mu = real depth / apparent depth — paraxial plane-slab relation for the same surrounding medium
- LC = 1 MSD - 1 VSD — travelling-microscope vernier resolution
How to approach it
- 1Calculate microscope LC
- 2Identify which focus differences are real and apparent depth
- 3Form the ratio and check that ordinary glass gives mu greater than one
Common slip-ups that cost marks
- •Using absolute microscope readings instead of differences
- •Reversing real and apparent depth
- •Ignoring the stated vernier relation
🌟 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.
In a meter bridge, resistance 2 ohm is in the left gap and balance occurs at 40 cm from the left end. Find the right-gap resistance.
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