Ray Optics · Virtual Lens Bench
Build principal-ray diagrams and predict image position, orientation and magnification for convex and concave thin lenses.
NCERT alignment: Class 12; chapter Ray Optics and Optical Instruments. Exam practice: JEE Main, JEE Advanced, NEET.
Learning objectives
Students should use the live simulator to test a quantitative prediction, read measurements and explain the limits of the model. Do not rely on the animation alone: calculate the expected result before adjusting controls.
Theory, equations and interpretations
Lens formula and signs
For a thin lens in air with the new Cartesian sign convention, an object to the left has u<0. Converging lens f>0 and diverging lens f<0. The image distance follows 1/f=1/v−1/u.
Important relation: 1/f = 1/v − 1/u; m = v/u = hᵢ/hₒ
Principal rays
One ray from the object top travels parallel to the principal axis and refracts through the second focal point for a convex lens (or appears to diverge from the first for a concave lens). A central ray travels approximately undeviated. Their intersection determines the paraxial image.
Real vs virtual
For a convex lens with the object beyond F, v>0 and m<0: the image is real and inverted. Inside F, v<0 and m>0: virtual upright image. A concave lens with a real object generally produces a virtual diminished image.
Object at focus
When |u|=f for a convex lens, 1/v=0 and the ideal image is at infinity. The drawn rays are then parallel and a finite image arrow is omitted.
Practical investigations
- Locate the image at 2F: Place a convex lens with f=20 cm and object distance 40 cm. Find v and m, then read the simulation.
- Inside the focus: Move the object from 30 cm to 12 cm while holding f=18 cm. Identify when the image becomes virtual.
- Switch lens sign: For u=−40 cm and |f|=20 cm, switch convex to concave and compare signs of v and m.
- Trace principal rays: Use the pen tool to extend the diverging refracted rays backward and identify the virtual image intersection.
Worked exam-style questions and answers
Q1. For a convex lens, u = −30 cm and f = +10 cm. Find v.
Options: A. −15 cm; B. +15 cm; C. +20 cm; D. −20 cm
Answer: B. 1/v=1/10+1/(−30)=1/15, so v=+15 cm.
Q2. An upright image formed by a convex thin lens from a real object is
Options: A. Always real; B. Virtual; C. Always reduced; D. Always at infinity
Answer: B. When object lies between focus and lens, rays diverge and the upright image is virtual.
Q3. A concave lens generally forms a real object image that is
Options: A. Real enlarged; B. Virtual diminished; C. Real inverted; D. At infinity
Answer: B. For a real object, concave lens v<0 and 0<m<1.
Q4. Magnification for a thin lens is
Options: A. u/v; B. f/u; C. v/u; D. v/f
Answer: C. With the Cartesian convention transverse magnification m=v/u.
Q5. At the focal point of a convex lens, the refracted rays from an on-axis point are
Options: A. Converging at F; B. Parallel; C. Returning to source; D. Circular
Answer: B. The ideal image lies at infinity; outgoing rays are parallel.
Q6. If u = −40 cm and v = +20 cm, magnification is
Options: A. +2; B. −2; C. +½; D. −½
Answer: D. m=v/u=20/(−40)=−0.5, inverted and reduced.
Common misconceptions and limitations
Paraxial thin-lens approximation in air. Off-axis and thick-lens aberrations are excluded. The virtual image is drawn using backward dashed extensions.
All learning content is available free of charge. The simulation is a simplified educational model. Check assumptions and units before applying a result. NANDAX SimStudio is not affiliated with NCERT or examination boards.
Teacher classroom use
Ask students to form a hypothesis, vary one parameter at a time, keep a record of graph readings, explain any change and compare results with the analytic relation. The on-screen worksheet offers questions with an answer key.