Optical Instruments

An optical instrument, in the sense used throughout the rest of this chapter, is any device built from one or more lenses (or, for a telescope, possibly a mirror in place of the main lens) whose purpose is to increase the angle subtended at the eye by an object, compared with the angle the same object would subtend if viewed by the unaided eye, so that the object appears larger and its detail becomes easier to resolve. This increase is measured by the magnifying power (or angular magnification) $M$ of the instrument, defined as the ratio of the angle $\beta$ subtended at the eye by the final image seen through the instrument to the angle $\alpha$ that the object itself would subtend if viewed directly, unaided, from the eye's normal near point: $M=\frac{\beta}{\alpha}.$ Note that this is a genuinely different quantity from the lateral (linear) magnification $m=h_i/h_o$ used earlier for a single mirror or lens -- magnifying power compares angles subtended at the eye, which is what actually determines how large or how resolvable an object looks to an observer, and is the quantity always quoted for microscopes and telescopes. The instruments taken up in the remaining sub-sections -- the simple microscope, the compound microscope, and the refracting and reflecting astronomical telescope -- are all, in the end, just particular combinations of one or two converging lenses (or a c …