A converging lens has a focal length of 46.0 cm. Locate the images for the follo

Question

A converging lens has a focal length of 46.0 cm. Locate the images for the following object distances, if they exist. Find the magnification. (Enter 0 in the q and M fields if no image exists.)

(a) 46.0 cm

q=____cm

M =___

Select all that apply to part (a).

real, virtual, upright, inverted, no image

(b) 5.41 cm

q = ____cm

M = ____

Select all that apply to part (b). real, virtual, upright, inverted, no image

(c) 92.0 cm

q = ___cm

M = ___

Select all that apply to part (c). real, virtual, upright, inverted, no image

Explanation / Answer

(a) The object is at the focal point of the lens and therefore light from the object emerges from the lens as a parallel beam. There is therefore no image.
(b) The lens equation is
1/u + 1/v = 1/f
where u is the object distance, v is the image distance and f is the focal length. The convention I use is that distances to real objects and images are positive while distances to virtual objects and images are negative. The focal length of a convex lens is positive and the focal length of a concave lens is negative.
1/5.41+ 1/v = 1/46
1/v = 1/46 - 1/5.41 = -0.163
v = -6.13 cm
The image is virtual and upright.
Magnification = v/u = 6.13/5.41 = 1.13
(c) 1/u + 1/v = 1/f
1/92 + 1/v = 1/46
1/v = 1/46 - 1/92 = 0.010
v = 100 cm
The image is real and inverted.
magnification = v/u = 100/92 = 1.08

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