GEOMETRICAL OPTICS - Lenses & Mirrors

Oct 25, 2026

Uploaded by Patrick

Comprehensive notes on geometrical optics covering convex and concave lenses and mirror types, including convex mirror and concave mirror concepts. Explains core ray-diagram terminology (principal axis, principal focus, focal length, optical centre, centre of curvature) and the formation of real versus virtual images for key object positions (between f and 2f, at f, at 2f, at infinity). Derives lens power and lens formula sign conventions, introduces magnification, and describes chromatic aberration and its correction using a chromatic doublet.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages12

Reading Time30 min

AccessFree to download

Convex lenses

Basic ray diagram terms

Power of a lens

Ray diagrams and image formation

Lens formula and sign convention

Magnification

Chromatic aberration

Concave lenses

Diverging lens overview

Basic ray diagram

GEOMETRICAL OPTICS ([http://www.a-levelphysicstutor.com/optics-convx-lnss.php](http://www.a-levelphysicstutor.com/optics-convx-lnss.php)) Convex lens Concave lens Plane mirror Convex mirror Concave mirror Convex Lenses | types | basic diagram | | power | ray diagrams | | | --- | --- | --- | --- | --- | --- | | lens formula | magnification | | chromatic aberration | | | | | | | | | | Types of lenses All four types of convex lens are converging lenses. That is, they bring parallel rays of light to a focus, producing a real image. Basic Ray Diagram The basic ray diagram for a convex lens introduces a number of important terms: principal axis-the line passing through the centres of curvature of the lens principal focus-a point on the principal axis where rays of light parallel to the principal axis converge focal length-the horizontal distance between the principal focus and the optical centre of the lens optical centre-an imaginary point inside a lens through which a light ray is able to travel without being deviated centre of curvature-the centre of the sphere of which the lens surface is a part Power of a Lens The power P of a lens is the inverse of its focal length f. Since f is measured in metres 'm' the units of lens power are m-1 . The power also depends on the type of lens. Convex lenses have positive powers. Concave lenses all have negative powers. For example, a 10 cm focal length convex lens has a power of +10 m-1; while a 20 cm focal length concave lens has a power of-5 m-1 . Ray diagrams To understand ray diagrams it is important to know something about images. Images come in two categories : real images-are produced from actual rays of light coming to a focus (eg a film projected onto a screen) virtual images-are produced from where rays of light appear to be coming from (eg a magnifying glass image) Ray diagrams are constructed by taking the path of three distinct rays from a point on the object: note-the lens is considered to be so thin as to be represented by the axis of the lens(green) A) a ray passing through the optical centre of the lens B) a ray parallel to the principal axis, which refracts through the lens, passing through the principal focus C) a ray passing through the principal focus(on the same side as the object) and being refracted through the lens, emerging parallel to the principal axis. The diagrams(below) represent the formation of an image from : | object between f and the lens (magnifying glass)

The image is the same side of the lens as the object and is upright, virtual and magnified. | object at f

The image is formed at infinity from parallel rays that do not converge. Therefore no image is formed. | | --- | --- | | object between f and 2f (projector)

The image is on the opposite side of the lens than the object. It is real, inverted and magnified. | object at 2f
The diagram is very similar to the left one, showing the three construction rays.
This time the image is the same
distance behind the lens as the object is in front.
As before, the image is inverted and real, but is the same size as the object. | | object at infinity
The image is formed at the focal point of the lens. It is real, inverted and diminished in size. | | The Lens Formula When using this equation a sign convention must be obeyed: Distances from lenses to real objects & real images are positive. Distances from lenses to imaginary objects and imaginary images are negative. Focal lengths of convex lenses are positive. Focal lengths of concave lenses are negative. | The focal length f of a lens can be found quite accurately by moving an illuminated object in front of a lens so that an image is cast on a screen.
By taking readings of image and object distances for different positions, a graph can be drawn.

Plotting 1/u against 1/v gives a straight line with a negative gradient. The focal leng

FAQs

What are the principal focus and focal length for a lens?

The principal focus is the point on the principal axis where rays parallel to the principal axis converge. The focal length is the horizontal distance between this focus and the optical centre of the lens.

How do real and virtual images differ in ray diagrams?

Real images come from actual rays converging at a focus, while virtual images come from the apparent point where rays seem to originate when extended backward.

What determines lens power and why can convex and concave lenses have opposite signs?

Lens power P is the inverse of focal length f. Since the focal length of convex lenses is taken as positive and concave lenses as negative, convex lenses have positive power while concave lenses have negative power.

Oct 25, 2026

Uploaded by Patrick