Geometric Optics Virtual Lab Guide

PhysicsIntermediateReading time: 3 min

Overview

The Convex Lens Imaging experiment is one of the most classic experiments in geometric optics. By changing the distance from the object (usually a candle) to the lens, we can observe images with different properties. This experiment aims to help you summarize how the relationship between object distance and focal length determines the properties of the image.

Background

As early as over 400 BC, the famous ancient Chinese thinker Mozi recorded the 'pinhole imaging' phenomenon in 'Mo Jing', explaining the principle of light propagation in straight lines. In the West, scientists such as Kepler and Newton further perfected the geometric optics theory of lens imaging, laying the foundation for the development of modern telescopes, microscopes, and photography technology.

Key Concepts

Focus (F) & Focal Length (f)

f

The point where light rays parallel to the principal axis converge after passing through a convex lens is called the focus. The distance from the center of the lens to the focus is the focal length.

Object Distance (u)

u

The horizontal distance from the center of the object (candle) to the center of the lens.

Image Distance (v)

v

The horizontal distance from the image position to the center of the lens. Real images are on the right side of the lens, and virtual images are on the left side.

Real vs Virtual

\text{Real vs Virtual}

A real image is formed by the convergence of actual light rays and can be captured on a screen; a virtual image is formed by the convergence of the reverse extensions of light rays and can only be observed directly with the eyes.

Formulas & Derivation

Lens Equation

\frac{1}{u} + \frac{1}{v} = \frac{1}{f}

Algebraic formula describing the quantitative relationship between object distance, image distance, and focal length.

Magnification Formula

m = -\frac{v}{u}

The ratio of image height to object height. If

m

is negative, it indicates an inverted real image; a positive value indicates an upright virtual image.

Experiment Steps

1
Explore Conditions for Reduced Real Image
Set focal length $f=35\text{cm}$ . Drag the candle to $u=80\text{cm}$ (i.e., $u > 2f$ ). Observe the image behind the lens on the right. Is the image inverted or upright? Is it magnified or reduced?
2
Find Real Image of Same Size
Adjust the candle position so that the object distance exactly equals twice the focal length ( $u = 2f = 70\text{cm}$ ). Observe if the image size is exactly the same as the object? Note the value of image distance $v$ at this time.
3
Explore Magnified Real Image
Continue moving the candle closer to the lens so that it is between one focal length and two focal lengths ( $f < u < 2f$ ). Observe the change in the image. You will find that the image becomes ____, and the image distance $v$ becomes ____?
4
Observe No Imaging Point
Place the candle at the focus ( $u = f = 35\text{cm}$ ). Observe the refracted rays, you will find they are parallel to each other. Can you still see a clear image on the screen at this time?
5
Explore Magnified Virtual Image
Move the candle inside the focus ( $u < f$ ). At this time, there is no light convergence on the right side, but virtual line convergence appears on the left side. This is the working principle of a magnifying glass. Is the image upright or inverted at this time?

Learning Outcomes

Master the three typical cases of convex lens imaging and their application conditions
Understand how image distance and image size change continuously when object distance changes
Be able to perform simple quantitative calculations using the lens imaging formula
Clarify the essential difference between virtual and real images in optical path evolution

Real-world Applications

Camera: When $u > 2f$ , forms an inverted, reduced real image
Projector: When $f < u < 2f$ , forms an inverted, magnified real image
Magnifying Glass: When $u < f$ , forms an upright, magnified virtual image
Telescope/Microscope: Realizes magnified imaging of distant or microscopic objects through the combination of multiple sets of lenses

Common Misconceptions

Misconception

Blocking the upper half of the lens with a baffle leaves only half of the image on the screen

Correct

Incorrect. The image is still complete, but the brightness of the image will dim due to the reduced luminous flux.

Misconception

Real images are always reduced, distinct virtual images are always magnified

Correct

Incorrect. Real images can be reduced (camera) or magnified (projector). However, for a single lens, upright virtual images are indeed always magnified.

Ready to start?

Now that you understand the basics, start the interactive experiment!

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