• summary_type: concept
• word_count: 200

Refraction at a single spherical surface is governed by n_{2}/v - n_{1}/u = (n_{2} - n_{1})/R. Applying this formula twice (for both surfaces of a lens) yields the lens maker's equation: 1/f = (n_{2}/n_{1} - 1)(1/$R_{1}$ - 1/$R_{2}$), which connects focal length to the geometry and material of the lens. The thin lens formula 1/v - 1/u = 1/f differs from the mirror formula by the sign on the 1/u term. Power P = 1/f (in dioptres when f is in metres) provides a convenient way to analyze lens combinations: for thin lenses in contact, P = $P_{1}$ + $P_{2}$. For separated lenses at distance d, P = $P_{1}$ + $P_{2}$ - dP_{1}$$P_{2}. A critical concept is that a convex lens becomes diverging when the surrounding medium has a higher refractive index than the lens material (e.g., air bubble in water). The minimum distance between a real object and its real image through a convex lens is 4f. These concepts form the backbone of most JEE ray optics problems.