A 1.40-cm-tall object is placed along the principal axis of a thin convex lens of 13.0 cm focal length.If the object distance is 19.2 cm,which of the following best describes the image distance and height,respectively?
A)7.75 cm and 4.34 cm
B)40.3 cm and 2.94 cm
C)7.75 cm and 7.27 cm
D)9.16 cm and 4.34 cm
E)41.4 cm and 0.668 cm

Question

Quizplus · Accepted Answer

Using the lens formula $ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} $, where $ f $ is the focal length, $ v $ is the image distance, and $ u $ is the object distance, we can find the image distance. Given $ f = 13.0 $ cm and $ u = -19.2 $ cm (object distance is taken as negative in the lens formula), solving for $ v $ gives us $ v \approx 40.3 $ cm. To find the image height, we use the magnification formula $ m = \frac{v}{u} = \frac{h_i}{h_o} $, where $ h_i $ is the image height and $ h_o $ is the object height. Given $ h_o = 1.40 $ cm, solving for $ h_i $ gives us $ h_i \approx 2.94 $ cm.

A 140-Cm-Tall Object Is Placed Along the Principal Axis of a a Thin