Thin lens formula

Using the thin lens formula to locate the image formed by a convex lensDifferent kinds of lenses produce different image properties: real or virtual, upright or inverted, and magnified or reduced. Each configuration also produces an image at a particular location. How can you predict the location of an image? The relationship between the object distance do, the image distance do, and the focal length f of the lens is called the thin lens formula. If you know two of these quantities, you can use the thin lens formula to calculate the third quantity. Equation (21.3) is also called the Gaussian lens formula. Read the text aloud Show What is meant by a “thin lens”?
(21.3) 1 d o + 1 d i = 1 f
do  = object distance (m)
di  = image distance (m)
f  = focal length (m)
Thin lens formula
A convex lens will form an image of a distant object at (or near to) the focal pointWhat happens to the location of the image when the object is moved further and further away from the lens? As you can see in the figure at right, when the object is moved to do = 260 cm—which is 6.5 times larger than the focal length of the lens—the image is located slightly beyond the far focal length. As the object is placed further and further away from the lens—as the object distance “goes to infinity”—its images will be produced closer and closer to the focal point. Read the text aloud Show Objects at infinity
A student has a convex lens but does not know its focal length. She sets up a light source 75 cm in front of the lens and then uses an index card to determine that it produces an image on the other side of the lens 37.5 cm away from the lens. What is the focal length of the lens?
Asked: focal length f of the lens
Given: Object distance do = 75 cm; image distance di = 37.5 cm
Relationships:
1 d o + 1 d i = 1 f
Solution: Insert the values into the thin lens equation:
1 f = 1 d o + 1 d i = 1 75 cm + 1 37.5 cm =0.0133  cm 1 +0.0267  cm 1 =0.04  cm 1
Now take the inverse of both sides of equation to solve for focal length:
f= 1 0.04  cm 1 =25 cm
Answer: The focal length is 25 cm.
Read the text aloud
An object is placed 3 m away from a converging lens with a focal length of 2 m. How far away from the lens will the image appear?
  1. 0.5 m
  2. 1.2 m
  3. 2 m
  4. 6 m
Show
If the object in the previous problem was placed north of the lens, on what side of the lens would the image appear? Show
Use the thin lens formula to prove that the location of the image in the first example on page 1226 (the converging lens) is correct. Show

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