Examples for lenses
a.) A converging lens (convex) has a focal length of 14 cm. Looking through the lens, one sees an image 20 cm behind the lens. Where is the object?
Solution: Since the image is behind the lens, it is virtual and the distance di is negative. Using the formula, , one can solve for do.
do = 8.24 cm
b.) If the height of the object is 1.5 cm, what is the height of the image.
Solution: Using the formula, to get
hi = 3.64 cm, upright
A real image of a coin is observed 34 cm beyond a lens. The image height is 1.4 cm and it is known that the actual coin is 0.7 cm high. What is the focal length of the lens?
Solution: First, find the object distance using . Remember that since the image is real, that the image height is negative. ( do = 17 cm ). One can then use to find the focal length.
f = 11.33 cm
An object is place half way between a converging lens and it's focal point. The focal distance is 8 cm.
a.) Where is the image?
Solution: Use with 4 cm for do.
di = -8 cm
b.) What is the magnification?
m = 2
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