A ray of light is incident at a height $$h$$ above the principal axis of a lens (position indicated by dotted line) and deviates through $$30^\circ$$ as it passes through the lens. Find the focal length of the lens.
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PLACEHOLDER ANSWER - the answer is an expression in $$h$$. The incident ray is parallel to the axis and bends away from it, so the lens is diverging (concave). The emergent ray, extended backwards, passes through the focus on the incident side, so $$\tan 30^\circ = \frac{h}{|f|}$$. Hence $$|f| = \sqrt{3}\,h$$, i.e. $$f = -\sqrt{3}\,h$$.