A converging lens has a focal length of 29.0 cm. Locate the images for the follo

Question

A converging lens has a focal length of 29.0 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) 29.0 cm

q=______cm

M=____

Select all that apply to part (a).

real virtual upright inverted no image

(b)5.27 cm

q=______cm

M=____

Select all that apply to part (b).

real virtual upright inverted no image

(c) 160 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.

1/5.27 + 1/v = 1/29
1/v = 1/29 - 1/5.27 = -0.309
v = -6.44 cm
The image is virtual and upright.
Magnification = v/u = 6.44/5.27 = 1.22

(c) 1/u + 1/v = 1/f
1/160+ 1/v = 1/29
1/v = 1/29 - 1/160 = 0.068
v = 35.42 cm
The image is real and inverted.
magnification = v/u = 35.42/160 = 0.22

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