Define and use the terms focal length, principal axis and principal focus (focal point)

Published by Patrick Mutisya · 14 days ago

IGCSE Physics 0625 – Thin Lenses

3.2.3 Thin Lenses

Learning Objective

Define and use the terms focal length, principal axis and principal focus (focal point) for thin lenses.

Key Definitions

  • Principal Axis: The straight line that passes through the centre of a thin lens and is perpendicular to its surfaces.

  • Principal Focus (Focal Point): The point on the principal axis where parallel rays of light either converge (convex lens) or appear to diverge from (concave lens) after passing through the lens.

  • Focal Length (f): The distance between the principal focus and the optical centre of the lens. It is positive for convex lenses and negative for concave lenses.

Ray Diagram Conventions

When drawing ray diagrams for thin lenses, the following three rays are sufficient to locate the image:

  1. A ray parallel to the principal axis, which after refraction passes through (or appears to come from) the principal focus.

  2. A ray passing through the optical centre of the lens, which continues undeviated.

  3. A ray directed towards (or away from) the principal focus, which after refraction emerges parallel to the principal axis.

Mathematical Relationship

The lens formula relates object distance (\$u\$), image distance (\$v\$) and focal length (\$f\$):

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

Sign conventions for IGCSE:

QuantityPositive whenNegative when
Object distance (\$u\$)Object is on the incoming‑light side of the lensObject is on the opposite side (virtual object)
Image distance (\$v\$)Image forms on the opposite side of the lens from the object (real image)Image forms on the same side as the object (virtual image)
Focal length (\$f\$)Convex (converging) lensConcave (diverging) lens

Using the Terms in Calculations

Example: A convex lens has a focal length of \$+8\ \text{cm}\$. An object is placed \$24\ \text{cm}\$ from the lens. Find the image distance and describe the image.

  1. Insert values into the lens formula:

    \$\frac{1}{8} = \frac{1}{v} + \frac{1}{24}\$

  2. Rearrange:

    \$\frac{1}{v} = \frac{1}{8} - \frac{1}{24} = \frac{3-1}{24} = \frac{2}{24} = \frac{1}{12}\$

  3. Thus \$v = +12\ \text{cm}\$ (positive → real image on the opposite side).

  4. Interpretation: The image is real, inverted, and reduced in size, located \$12\ \text{cm}\$ behind the lens on the principal axis.

Suggested Diagram

Suggested diagram: Ray diagram for a convex lens showing the principal axis, principal focus (F), optical centre (O), an object (U) placed left of the lens, and the resulting real image (I) formed on the right side.

Quick Revision Checklist

  • Identify the principal axis in any lens diagram.

  • Locate the principal focus on the principal axis, remembering its position differs for convex and concave lenses.

  • Measure or calculate the focal length as the distance between the principal focus and the optical centre.

  • Apply the lens formula with correct sign conventions.

  • Use the three standard rays to construct accurate ray diagrams.