Investigating angular magnification in a low-cost Keplerian telescope using smartphone afocal photography

Geometric optics is often difficult for junior high school students because affordable, hands-on learning instruments are limited. To support physics teachers in resource-limited settings, we developed a practical, low-cost Keplerian telescope project. This study measured and compared image magnification using three eyepiece lenses with nominal focal lengths of 23 mm, 20 mm, and 12 mm and diameters of 20 mm, 8.5 mm, and 9.7 mm, respectively. After recalibration, their actual focal lengths were 17 mm, 13 mm, and 10 mm. A fixed objective lens with a focal length of 40 cm and a diameter of 85 mm was used. A within-subjects experimental design was used with 10 objects for each eyepiece configuration. Empirical magnification was measured using smartphone afocal photography and a Vernier Caliper, then calculated as the ratio of the image height through the telescope to the image height without it ( M = h ′/ h ). All configurations produced magnifications close to theoretical values, with deviations of 1.16%–4.18%. The 10 mm eyepiece produced the highest magnification: 38.33×, compared with the theoretical 40× (4.18% deviation; R 2 = 0.9912). The 13 mm eyepiece produced 28.92× versus 30.8× (1.79%; R 2 = 0.7536), while the 17 mm eyepiece produced 22.61× versus 23.5× (1.16%; R 2 = 0.9771). The 17 mm eyepiece was most suitable for junior high school optics practicums because of its accuracy, wide field of view, and low cost.This validated activity enables students to investigate focal length experimentally and transform abstract optical equations into engaging, measurable classroom experiences.