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“Ray Optics: Lens and Mirror Systems in Depth” is available to Standard subscribers.

Beyond the textbook: lenses measured by the displacement method, a lens in a liquid, a lens cut in two or silvered on one face, apparent depth through layers, and the full derivations for the prism. The level of JEE Advanced, A-Level and IB Higher Level, with a full timed paper.

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Read the first lesson freeLens experiments and lenses in other media

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Lens experiments and lenses in other media: The displacement method finds a focal length from two sharp images, $f = \dfrac{D^2 - d^2}{4D}$

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This is an extra course for Ray Optics and Optical Instruments. Its main courses are open to everyone:

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Silvered lenses, split lenses and layered media: A lens with a silvered face is a mirror of power

2P_{lens} + P_{mirror}

, because the light crosses the lens twice. A lens cut across keeps its power in two pieces, and a lens cut along its axis keeps its focal length. Layers of thickness

t

and index

n

seem

\dfrac{t}{n}

thick.

Prisms in depth and ray-tracing traps: A prism deviates light by

\delta = i + e - A

. The deviation is least when the ray passes symmetrically, and then

n = \dfrac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}}

. Light can leave the second face only if

A < 2C