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c.real with a transverse magnification of –1.77×

d.real with a transverse magnification of 0.56×

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Appendix 1.1

Quick Review of Angles, Trigonometry, and the Pythagorean Theorem

It is useful to review a few basic principles of geometry and trigonometry to help with our understanding of image magnification. Recall that a circle is divided angularly into 360°, which corresponds approximately to 6.28 radians. Converting between degrees and radians is frequently necessary when optics problems are being solved. A degree is subdivided into 60′ (minutes); each minute is subdivided into 60″ (seconds).

The sum of the angles in a triangle equals 180°, or π radians. For any right, or right-angled, triangle with sides a, b, and c (Fig 1-72) and angle θ between sides b and c, the trigonometric function is defined as follows: