Lab: Geometric Optics on an Optical Bench

Light leaving every point on an object spreads out in a cone. A converging lens bends that cone back together, but it only refocuses to a sharp point at one specific distance behind the lens, the image distance di, which depends on the object distance do and the focal length f through 1/do + 1/di = 1/f. Move the screen even a centimeter off that spot and the cones of light haven't finished converging or have already crossed and started spreading again, so you get a blurred patch instead of a point. That is why focus happens at exactly one spot: it's the one place where geometry and the lens equation agree.

To find f directly, use a distant object, like a window across the room, so do is effectively infinite and 1/do is essentially zero. The lens equation collapses to 1/di = 1/f, meaning the image lands right at the focal point. Slide a screen behind the lens until that distant scene snaps into sharp focus, measure lens-to-screen distance, and that measurement is f itself, no calculation needed. For nearer objects, you measure pairs of do and di, then plot 1/di on the y-axis against 1/do on the x-axis. Rearranged, the thin lens equation is 1/di = -1/do + 1/f, a line with slope -1 and y-intercept 1/f, so f is just one divided by that intercept.

The refractive index lab uses the same bench logic but trades the screen for pins and angles: stick pins to mark the path of light entering a glass block, trace the ray bending at each surface, then measure the angle of incidence and angle of refraction with a protractor and apply Snell's law, n1 sin(theta1) = n2 sin(theta2), with air's index taken as 1. Both labs connect to the same unit theme: straighten a curved relationship into a line so a single slope or intercept hands you the physical constant you're after.