Question
A convex lens of focal length forms a real image at from itself. Find the object distance and the magnification — in under 45 seconds.
Solution — Step by Step
For a real image on the opposite side: . For a convex lens: . Object on the left: is negative.
So . Object is to the left of the lens.
The negative sign means the image is inverted, and the magnitude means the image is twice the size of the object.
Magnification: .
Why This Works
The lens formula plus the magnification formula solve nearly every “find the object/image distance” problem in JEE/NEET. Two formulas, three lines — that is the entire toolkit.
The sign convention (Cartesian: distances measured from the optical centre, leftward negative, rightward positive) keeps the algebra automatic. We never need to “decide” if the image is real or virtual — the sign of tells us.
45-second rule: Identify the unknown, plug in signs by Cartesian convention, solve. If comes out positive, image is real and on the opposite side. If negative, virtual and on the same side as the object.
Alternative Method — Newton’s Lens Formula
For problems where we know object and image distances from the focal points (not from the lens), Newton’s form is faster. But for standard lens problems with distances from the lens, the basic formula wins.
Common Mistake
The biggest trap is sign errors. Students often plug in instead of , getting nonsensical answers. Always assign the sign first based on which side the object/image is on.
Another classic: confusing the lens formula with the mirror formula . The minus sign vs plus sign trips up half the candidates in board exams.
NEET 2024 asked an identical structure with and image at — toppers wrote the answer in 30 seconds flat. Memorise the workflow: assign signs, plug in, simplify, read off.
For the magnification follow-up, gives both magnitude and orientation in one shot. No additional formula required.