Key relationship
n₂/v − n₁/u = (n₂−n₁)/R, with u=−d; m=n₁v/(n₂u).
Physics · Class 12
Curved boundary refraction
Ray Optics & Optical Instruments
Curvature and an index difference give an interface optical power. The focal object distance differs from the focal image distance because the two media have different indices.
Open the interactive experiment →Curved boundary refraction
வளைந்த எல்லையின் ஒளித்திறன் வளைவும் ஒளிவிலகல் எண் வேறுபாடும் சார்ந்தது.
Key notes, relationships and model limits
Remember
Curvature and an index difference give an interface optical power. The focal object distance differs from the focal image distance because the two media have different indices.
Common trap
A curved surface does not focus if the refractive indices match.
Model limits
Paraxial refraction; incident medium on left; R>0 means centre on right. Equal indices yield no focusing. Diagram is schematic; model distances are signed.
What you will learn
Use signed spherical-refraction distances.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
n₁=1,n₂=1.5,R=10 cm,d=40 cm gives v=60 cm.
Why this matters
The model connects curved boundary refraction with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
If the refractive indices are equal, the curved interface has?
- Maximum power
- Zero power
- Infinite power
Read the explanation
The surface-power term (n₂−n₁)/R vanishes.
Course connection: Class XII Chapter 9. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.