Lens combinations on an optical bench
PhysicsOpticsAges 14–15Virtual lab
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Combine two thin lenses in contact or a gap apart and find the focal length of the combination on a screen: 1/F = 1/f₁ + 1/f₂ − d/(f₁f₂), and P = P₁ + P₂ in dioptres for lenses in contact. Three practicals with needles and parallax removal: the focal length of a concave lens with a convex lens, the focal length of a convex mirror with a convex lens, and the refractive index of a liquid from a liquid lens between a convex lens and a plane mirror. Cartesian sign convention, distances in cm, results tables and self-checked tasks.
Lesson: Combination of thin lenses; Power of a lens; Optical bench practicals
What it shows
Lenses used together act like one lens. The first screen combines two thin lenses: in contact their powers add (P = P₁ + P₂, with P in dioptres = 1/f in metres), and with a gap d the equivalent focal length is 1/F = 1/f₁ + 1/f₂ − d/(f₁f₂). The other screens are bench practicals with needles and parallax removal: a concave lens and a convex mirror cannot form a real image alone, so a convex lens supplies one; a liquid between a convex lens and a plane mirror forms a plano-concave lens whose focal length gives the liquid's refractive index. Thin lenses and paraxial rays are assumed.
How to use
On Two lenses, choose Lens L₁, Lens L₂ and the gap d, move the screen S until the window is sharp and press Record. On the practical screens, press Move your eye and move the needle (or the mirror) until the tips stay together, then press Record: first without the second element, then after Insert L₂, Insert mirror or Add liquid. Type your result in the task box and press Check.
Parameters you can change
- Screen Two lenses, Concave lens f, Convex mirror f, Liquid lens μ
- Lens L₁ (two-lens screen) Convex +10 cm, Convex +15 cm, Convex +20 cm, Convex +25 cm, Convex +30 cm, Convex +50 cm, Concave −20 cm, Concave −30 cm, Concave −50 cm
- Lens L₂ (two-lens screen) Convex +10 cm, Convex +15 cm, Convex +20 cm, Convex +25 cm, Convex +30 cm, Convex +50 cm, Concave −20 cm, Concave −30 cm, Concave −50 cm
- Gap d between the lenses 0–20 cm
- Focal length of the convex lens L₁ (practicals) 10–20 cm
- Focal length of the concave lens (to be measured) -40–-15 cm
- Radius of curvature of the convex mirror (to be measured) 20–50 cm
- Liquid Water, Ethanol, Glycerol
Questions to explore
- Why does a concave lens need a convex lens to form a real image that a needle can locate?
- Two lenses of +20 cm and +30 cm are in contact: what is the power of the combination?
- Why does the image of the needle fall back on the needle when it is at the focal plane of the lens on a plane mirror?
