A concave mirror has a radius of curvature of 62.5 cm. Consider the image that w

Question

A concave mirror has a radius of curvature of 62.5 cm. Consider the image that would be formed using that mirror of an object placed at three different distances from the miror. For each of the following, calculate the image distance s' and the magnification m; then provide a drawing showing the position of the mirror, its focus, the object, the image, and try to get the relative sized of the object and correct. Is the image magnified or demagnified? Is the image real or virtual?

a) The object distance is 96.0 cm.

b) The object distance is 42.0 cm.

c) The object distance is 9.6 cm. Note that this is inside the focus--expect some weird things to happen.

d) Describe the changes in the image position and size as the object is moved. Do you see a general rule emerging?

Explanation / Answer

f = R/2 = 62.5/2 = 31.25 cm

a) u = 96 cm

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/31.25 - 1/96

v = 46.33 cm (object distance)

magnification, m = -v/u

= -46.33/96

= -0.48

image is real and demagnified.

b) u = 42 cm

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/31.25 - 1/42

v = 122.1 cm (object distance)

magnification, m = -v/u

= -122.1/96

= -1.27

image is real and magnified.

c) u = 9.6 cm

Apply, 1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/31.25 - 1/9.6

v = -13.86 cm (object distance)

magnification, m = -v/u

= -(-13.86)/96

= 0.144

image is virtual and demagnified.

d)As the object moves towards focal point image moves towards infinite.

when the object moves beyond the focal point again image distance decreases and approches zero.

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