ou have encouraged your little sister, who has just gotten glasses for her sever

Question

ou have encouraged your little sister, who has just gotten glasses for her severe near-sightedness, to give you those glasses so you can play with them. You know from the prescription of the optometrist that each lens is of -6.00 diopters in strength. You then hold the glasses at arms length and playfully look through them at your sister's face when it is 495.0 mm on the other side of the glasses.
a) How far from the glasses, in mm, will your sisters's face appear to be? (In your answer, ignore sign conventions about distance of images from lenses.)

b) If your sister's face is 180. mm-tall, how tall will it appear to be in the image (in mm)?

Explanation / Answer

the focal length is
f = - 1/6 = 0.16666 m = 16.666 cm
di = distance of image, do = distance of object

Image size I / object size O = I/O = - di/do = - f/(-f + do)
I/O = 16.666/(16.666 + 49.5) = 0.25188.

The image distance = do*0.2614 = 495*0.25188 = 124.6846 mm
The image size = 180*0.25188 = 45.3398 mm

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