Lesson 6 of 11 · 12 min
Thin lenses: lens maker's formula and thin lens formula
NCERT § "Refraction by a Lens"
Kabir holds his lens between the candle and the wall and slides it until a sharp, upside-down flame appears. Its focal length is written nowhere on the lens, yet the glass and its curves decide it.
The lesson in notes
In short
Lens maker's formula: 1/f = (n₂₁ − 1)(1/R₁ − 1/R₂), where n₂₁ is the refractive index of the lens material relative to the surrounding medium.
For a biconvex lens with light from the left, R₁ is positive and R₂ is negative; for a biconcave lens, R₁ is negative and R₂ is positive.
A convex (converging) lens has positive f and a concave (diverging) lens has negative f in this convention.
Thin lens formula: 1/v − 1/u = 1/f. Note the minus sign, unlike the mirror equation.
Linear magnification of a lens is m = h′/h = v/u, again without the minus sign used for mirrors.
When a lens is placed in a liquid, n₂₁ becomes n_lens/n_liquid, so the focal length changes. If the liquid's n equals the lens's n, the lens has no effect (f becomes infinite); if the liquid's n is larger, a convex lens behaves as a diverging lens.
A convex lens gives a real inverted image for objects beyond F and a virtual erect enlarged image for objects between F and the lens; a concave lens always gives a virtual, erect, diminished image of a real object.