Lenses, Vision and Optical Instruments
Big idea: a lens changes the directions of many rays in a controlled way, allowing an image to form on a screen, the retina or a sensor.
Learning goals
- distinguish converging and diverging lenses;
- use principal rays and the thin-lens equation;
- relate focal length to optical power;
- explain accommodation and common vision corrections;
- describe cameras, magnifiers and microscopes as lens systems.
Lens language
A converging lens is thicker near its centre and brings parallel paraxial rays toward a principal focus. A diverging lens spreads them as if they came from a focus on the incident side. Focal length $f$ is measured from optical centre to focus. Optical power is $P=1/f$ when $f$ is in metres; its unit is the dioptre.
Images and equations
For a thin lens, $1/f=1/d_o+1/d_i$. The magnification is $m=h_i/h_o=-d_i/d_o$. A positive screen distance describes a real image; a virtual image cannot be caught on a screen because the emerging rays only appear to meet.
Three principal rays
- A ray parallel to the axis leaves through the far focus.
- A ray through the near focus leaves parallel to the axis.
- A ray through the optical centre continues approximately straight.
Construction workflow: draw the axis and lens; mark both foci; draw any two principal rays from the top of the object; their intersection locates the top of the image; identify real/virtual, upright/inverted and enlarged/reduced.