Concave Lens Image Formation

Lens Laboratory

Object selection

✏️Pencil

▼

✏️Pencil

🐧Penguin

⬆️Arrow

💡Light

Lens controls

Object distance from lens, u (cm)

Radius of curvature (cm)

Index of refraction

Lens diameter (cm)

Ray controls

Marginal Principal Many None

Simulation Viewport

Drag the object left/right • Observe rays • Observe the virtual image

Focal points (F) Image Labels

Observation Table

Updates automatically whenever the simulation changes

Object distance u	Focal length f	Image distance v	Magnification	Image height h′	Image formed	Nature	Size

Control Panel

Concave Lens ChallengeLEVEL 1

Question JSON will load from the URL. Set the simulation values yourself, then submit.

Image distance v (cm)

Magnification m

Image type

Image nature

Image size

Adjust the simulation if needed, then submit your answer.

Book Back ProblemSOLVED

Book back question JSON will load from the URL. The answer will be shown automatically.

No problem loaded yet.

Try your own input parameters

Object type Object distance u (cm) Object height (cm) Radius of curvature (cm) Index of refraction Diameter (cm)

Help Guide

Change Object Distance (u): Drag the object horizontally in the simulation area, or use the stepper inputs / number input for Object distance from lens, u in the left panel.
Set Radius of Curvature (R): Adjust the Radius of curvature stepper on the left to modify the curvature of the lens surface.
Set Refractive Index (n): Adjust the Index of refraction stepper to change the lens material's optical density.
Choose Ray Mode: Select Marginal (3 edge/center rays), Principal (3 construction rays), Many (17 rays), or None in the Ray controls.
Read Observation Table: Check the table below the viewport. It updates live with object distance, focal length, image distance, magnification, type, nature, and size.

Virtual Image

An image formed when diverging light rays are projected backwards (dashed grey lines). It cannot be projected onto a screen and is formed on the same side of the lens as the object.

Erect Image

An upright image pointing in the same vertical direction as the object. The magnification (m) value is positive.

Diminished Image

An image that is smaller than the original object. The magnification magnitude |m| is less than 1.

Concave Lens Physics

Follows 1/f = 1/v - 1/u (Cartesian). The focal length (f) and image distance (v) are always negative for real objects, producing virtual, erect, and diminished images.

📝 Test Yourself Mode

Loads challenges from the URL. Set the simulation controls manually to match the question parameters, calculate the expected values, enter them in the fields, and click Submit to validate.

🧮 Problem Solver Mode

Displays book-back questions. Click Try Your Own Problem to unlock the inputs and customize the given values to solve any custom lens problem dynamically.

Simulation Viewport

Principle Diagram

Principle of Concave Lens