Lens Formula — Thin lens, power, combination
Ray Optics
12
JEE Qs
8%
Hard
75
min
Master the Cartesian sign convention thoroughly, as almost all errors stem from incorrect sign usage in ray optics problems.
🧮 Key Formulas
✅ Key Points for JEE
- 1Strictly follow the Cartesian sign convention for all distances (u, v, f, R); origin at optical center, incident light from left is positive direction.
- 2Focal length (f) is positive for convex (converging) lenses and negative for concave (diverging) lenses.
- 3Magnification (m) indicates image nature: m > 0 for virtual/erect image, m < 0 for real/inverted image. |m| > 1 for magnified, |m| < 1 for diminished.
- 4For the Lens Maker's Formula, ensure correct signs for R₁ and R₂ based on the curvature of each surface (center of curvature on the side of incident light implies positive R).
- 5When lenses are combined in contact, their powers simply add up, making it easier to find the equivalent focal length.
⚠️ Common Mistakes
- ✕Sign errors due to inconsistent application of the Cartesian sign convention, especially for object distance (u) and radii of curvature (R).
- ✕Confusing the lens formula (1/v - 1/u = 1/f) with the mirror formula (1/v + 1/u = 1/f).
- ✕Not converting focal length to meters when calculating power in Diopters (P = 1/f).
- ✕Incorrectly applying the refractive index ratio in the Lens Maker's Formula (n_lens/n_medium).
- ✕Forgetting to multiply individual magnifications for lens combinations.
📝 Practice Questions
See allQ46.The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R = 2 m . Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ m/s2 .
Q27.A spherical surface of radius of curvature R, separates air from glass (refractive index = 1.5 ). The centre of curvature is in the glass medium. A point object ' O ' placed in air on the optic axis of the surface, so that its real image is formed at ' I ' inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to (1) 5 R (2) 3 R (3) 1.5 R (4) 2 R
Q32.Given is a thin convex lens of glass (refractive index μ ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that 2025 (22 Jan Shift 1) JEE Main Previous Year Paper the image gets formed on the object itself ? (1) R/μ (2) R/(2μ −3) (3) μR (4) R/(2μ −1)
Q42.In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to |R1| and |R2|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is (1) 1 − + |R2| |R2| 6 ( |R1|1 1 ) (2) −16 ( |R1|1 1 ) (3) 1 + − |R2| |R2| 6 ( |R1|1 1 ) (4) −16 ( |R1|1 1 )
Q29.A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4 D then the power of a part of the divided lens is (1) D (2) 8D (3) 2D (4) 4D
Q29.Given a thin convex lens (refractive index μ2 ), kept in a liquid (refractive index μ1, μ1 < μ2 ) having radii of curvatures |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place? (1) μ1|R1|⋅|R2| (2) μ1|R1|⋅|R2| μ2(|R1|+|R2|)−μ1|R2| μ2(|R1|+|R2|)−μ1|R1| (3) (μ2+μ1)|R1| (4) μ1|R1|⋅|R2| (μ2−μ1) μ2(2|R1|+|R2|)−μ1√|R1|⋅|R2|
NCERT Chapters
- Class 12 Physics Part 2, Chapter 9: Ray Optics and Optical Instruments