Key relationship
P = P₁+P₂−dP₁P₂; contact d=0. Plane-mirror double pass: P=2P₁−2dP₁².
Physics · Class 12
Compound optical power
Ray Optics & Optical Instruments
Lens powers add in contact. Separation introduces an extra term and shifts the principal planes. A plane mirror immediately at a thin lens sends light through that same power twice.
Open the interactive experiment →Compound optical power
தொடுபடும் லென்சுகளின் திறன்கள் சேரும். இடைவெளி இருந்தால் கூடுதல் திருத்தம் தேவை.
Key notes, relationships and model limits
Remember
Lens powers add in contact. Separation introduces an extra term and shifts the principal planes. A plane mirror immediately at a thin lens sends light through that same power twice.
Common trap
Do not add focal lengths; add powers, with the separation correction when required.
Model limits
Thin paraxial optics; distances consistently in cm before converting power to D. Plane-mirror return uses L(P)·T(2d)·L(P) in an unfolded path; effective principal planes may shift.
What you will learn
Compare contact, separated and coincident double-pass systems.
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
Two20 cm lenses in contact give f=10 cm; a20 cm and−20 cm pair is afocal.
Why this matters
The model connects compound optical power with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Two +5 D lenses in contact have combined power?
- 2.5 D
- 10 D
- 0 D
Read the explanation
Contact powers add:5+5=10 D.
Course connection: Class XII Chapter 9. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.