Light – Reflection and Refraction · Lesson 11 of 15
Refraction by Spherical Lenses
“Convex lenses gather rays while concave lenses politely send them apart.”
• Distinguish convex and concave spherical lenses. • Identify centres of curvature, principal axis, optical centre and aperture. • Explain the two principal foci and focal length of a lens. • Compare converging and diverging actions. • Estimate a convex lens's focal length safely.
A watchmaker's magnifier and a spectacle lens both use curved transparent surfaces to redirect light. Unlike a mirror, a lens forms images by refraction at two surfaces. Its shape decides whether a parallel beam gathers together or spreads apart.
A transparent material bounded by two surfaces, at least one of which is spherical.
Convex and Concave Lenses
A double convex lens bulges outward on both sides and is thicker at the middle than at the edges. It brings parallel rays together and is called a converging lens. A double concave lens curves inward on both sides and is thinner at the middle. It spreads parallel rays and is called a diverging lens.
Parts of a Spherical Lens
The centres of the two spheres whose surfaces form the lens, represented by C₁ and C₂.
The imaginary straight line passing through C₁ and C₂.
The central point O of a thin lens; a ray through O passes without appreciable deviation.
The effective diameter of the circular outline of the lens.
A lens has two principal foci because light may enter from either side. Rays parallel to the principal axis converge at F₂ after passing through a convex lens. Through a concave lens, they diverge as if from F₁ on the incident side. The distance OF is the focal length f.
Thin Lenses
The ray rules used here assume a thin lens with a small aperture: the aperture is much less than the radii of curvature, and C₁ and C₂ are treated as equally spaced from O. This simplified model lets both refractions be represented at the central lens line.
Estimating the Focal Length
Never look at the Sun directly or through a lens. A convex lens can focus intense light onto the retina and cause permanent injury.
Point a convex lens toward the Sun without looking through it. Move a paper screen on the opposite side until the smallest sharp bright image appears. The lens-to-screen distance approximates f because the Sun is effectively at infinity and sends nearly parallel rays. Remove the paper promptly because concentrated light can burn it.
Problem
Two convex lenses have focal lengths 10 cm and 25 cm. Which bends parallel rays more strongly?
- 1.A shorter focal length means rays meet closer to O.
- 2.Meeting closer requires a larger change in ray direction.
- 3.Therefore the 10 cm lens has the stronger converging action.
Quiz
Which lens is thicker at its centre?
How many principal foci does a lens have?
What happens to a ray through O of a thin lens?
Why is a concave lens called diverging?
What distance approximately gives f in the Sun-screen activity?
Practice Problems
- Classify a lens thinner at the centre. Solution: It is a concave, diverging lens.
- Why does a lens have two centres of curvature? Solution: Its two spherical surfaces belong to two spheres, each with its own centre.
- Describe the principal focus on each side of a convex lens. Solution: Parallel rays entering from either side converge at the focus on the opposite side, giving F₁ and F₂.
- Why is the Sun suitable for estimating f? Solution: Its great distance makes arriving rays nearly parallel, so a convex lens forms its image near the principal focus.
- Compare lenses with f = 8 cm and f = 40 cm. Solution: The 8 cm lens bends rays more strongly because it converges or diverges them over a shorter distance.
Key Takeaways
• A lens refracts light at two surfaces, at least one spherical. • Convex lenses converge and concave lenses diverge parallel rays. • A lens has two centres of curvature and two principal foci. • A central ray through O passes nearly undeviated in the thin-lens model. • Focal length is the distance from O to a principal focus. • Shorter focal length indicates stronger convergence or divergence.