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An equiconvex glass lens (μ = 1.5) has radius of curvature R = 20 cm for both surfaces. Its focal length in air is:

+20 cm. Applying Lens Maker's formula: 1/f = (1.5 - 1)(1/20 - 1/(-20)) = 0.5 × (2/20) = 1/20 ⇒ f = +20 cm.

Physics · Class 12 · JEE / NEET / AP Physics 2

Ray Optics: Spherical Mirrors & Lens Maker's Formula

Ray Opticsmodels light propagation as straight rays, analyzing image formation by reflection in mirrors and refraction through lenses using theLens Maker's Formula.

11. Visual Overview & Intuitive Discovery: Ray Optics: Spherical Mirrors & Lens Maker's Formula

In 1609, Galileo Galilei constructed a crude telescope from two glass lenses inside a lead tube and pointed it at the night sky. In a matter of weeks, he shattered 2,000 years of Aristotelian cosmology by discovering four moons orbiting Jupiter, craters on our Moon, and phases of Venus. Geometric optics transformed humanity's view of the cosmos.

Ray Optics: Prisms, Lenses & Total Internal Reflection: Gaussian Lens Formula, Mirror Formula, Lens Maker's Equation, Linear Magnification, Power of Lens — Ray Optics: Prisms, Lenses & Total Internal Reflection
Prism refraction and minimum deviation formula, convex lens ray tracing with lens maker's formula, and critical angle total internal reflection in optical fibers.
1Gaussian Lens Formula — 1/f = 1/v - 1/u
2Mirror Formula — 1/f = 1/v + 1/u with focal length f = R/2
3Lens Maker's Equation — 1/f = (μ₂/μ₁ - 1) · (1/R₁ - 1/R₂)
4Linear Magnification — m = v / u (for lens) and m = - v / u (for mirror)
5Power of Lens — P = 1 / f(in meters) measured in Diopters (D)

Interactive Study Prompts (Click to Explore)

Clickable

AI Deep Dive 🪄

22. Physical Mechanism Flowchart: Ray Optics: Spherical Mirrors & Lens Maker's Formula

Ray Optics: Spherical Mirrors & Lens Maker's Formula Step-by-Step Flowchart

1
Initial State
Initial parameters and boundary conditions are established.
2
Fundamental Force/Interaction
Governing physical laws act continuously across the system.
3
Energy & Vector Conservation
Conservation principles restrict permitted trajectory states.
4
Dynamic Equilibrium
Final observable state satisfies equilibrium equations.

Follow the numbered pipeline above. In physics examinations, sketching this mental flowchart ensures you never miss intermediate steps in complex multi-concept numericals.

33. Rigorous Mathematical Proofs & Governing Equations

Derivation — Derivation of Governing Formula for Ray Optics: Spherical Mirrors & Lens Maker's Formula

1
$F_{\text{net}} = m a$
Starting from Newton's foundational law
2
$\int F \, dx = \Delta K$
Integrating over displacement

Combination of Two Thin Lenses in Contact

\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2},\quad P_{\text{eq}} = P_1 + P_2

F = Equivalent focal length of the combined lens system
$P_{\text{eq}}$ = Net optical power in diopters

Core Physical Variables

Variable	Symbol	SI Unit
Energy	E	Joules (J)
Power	P	Watts (W)

Energy
Symbol
E
SI Unit
Joules (J)
Power
Symbol
P
SI Unit
Watts (W)

44. Medical Innovation: Corrective Eye Surgery and Cataract IOLs

Every year, millions of elderly people lose their vision due to cloudy cataracts. Eye surgeons use an ultrasound probe to emulsify the defective natural lens, and inject a folded synthetic Intraocular Lens (IOL) through a 2 mm incision. Using the Lens Maker's Formula ( $1/f = (\mu - 1)(1/R_1 - 1/R_2)$ ), ophthalmic engineers design custom curved silicone surfaces with exact diopter power to restore 20/20 vision.

Common mistake: Misconception: "If you cover the top half of a camera lens with black tape, you will only see the bottom half of the photograph." Covering half the lens still produces the COMPLETE image! Every single point on an object emits rays that strike all parts of the lens. The only effect of blocking half the lens is cutting the light gathering area in half, making the resulting image 50% dimmer (intensity halved).

55. Solved Standard & Advanced Exam Problems

Exam question · JEE Standard

Sample Question

Exam question · JEE Main & NEET

A convex lens of focal length 20 cm made of glass (μ = 1.5) is immersed in water (μ = 1.33). What is its new focal length in water?

A.+78.2 cm
B.+40.0 cm
C.+20.0 cm
D.-78.2 cm

Remember

Focal length of a convex lens is positive, while a concave lens has negative focal length.
When a glass lens (μ = 1.5) is immersed in water (μ = 1.33), its focal length increases by approximately 4 times.
If a lens is immersed in a liquid having the exact same refractive index as the glass, it becomes completely invisible and acts as a flat plane (f = ∞).

Check yourself

Question 1
An equiconvex glass lens (μ = 1.5) has radius of curvature R = 20 cm for both surfaces. Its focal length in air is: