Question

51) Consult Interactive Solution 26.51 to review the concepts on which this problems depends. A camera is supplied with two interchangeable lenses, whose focal lengths are 25.0 and 150.0 mm. A woman whose height is 1.66 m stands 7.50 m in front of the camera. What is the height (including sign) of her image on the image sensor, as produced by (a) the 25.0-mm lens and (b) the 150.0-mm lens?

Answer 1

the height of the woman is h = 1.66 m

The distance from the camera is u = 7.5 m

1)

The focal length of the lens is f = 25 mm = 0.025 m

The lens equation is

1/f = 1/u + 1/v

1/0.025 = 1/7.5 + 1/v

v = 0.0250 m

The magnification m = -v/u

m = -0.0250/7.5

m = -0.0033

The height of the image is h' = mh

h' = -0.0033*1.66 m

h' = -0.0054782 m

- sign indicates that the image is inverted

2)

The focal length of the lens is f = 150 mm = 0.15 m

The lens equation is

1/f = 1/u + 1/v

1/0.15 = 1/7.5 + 1/v

v = 0.154 m

The magnification m = -v/u

m = -0.154/7.5

m = -0.0205

The height of the image is h' = mh

h' = -0.0205*1.66 m

h' = -0.03403 m

- sign indicates that the image is inverted