The Thin-Lens Equation

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Presentation transcript:

The Thin-Lens Equation

The Thin-Lens Equation

The Thin-Lens Equation Because the two shaded triangles are right angles, the angle  must be the same for both. The triangles are similar. For similar triangles, the ratios of any two similar sides are the same:

The Thin-Lens Equation We have also shown that Combining the equations gives

The Thin-Lens Equation Finally this is written as the thin-lens equation:

Sign Conventions for Lenses & Mirrors In the thin-lens equation, the sign of the focal length can be either positive or negative, depending on the type of lens or mirror.

Sign Conventions for Lenses & Mirrors

Question 1 A lens creates an image as shown. In this situation, the object distance s is Larger than the focal length f Equal to the focal length f Smaller than focal length f Answer: A 8

Question 1 A lens creates an image as shown. In this situation, the object distance s is A) Larger than the focal length f B) Equal to the focal length f C) Smaller than focal length f Answer: A 9

Question 2 A lens creates an image as shown. In this situation, the image distance s is A) Larger than the focal length f B) Equal to the focal length f C) Smaller than focal length f Answer: A 10

Question 2 A lens creates an image as shown. In this situation, the image distance s is A) Larger than the focal length f B) Equal to the focal length f C) Smaller than focal length f Answer: A 11

Question 3 Light rays are converging to point 1. The lens is inserted into the rays with its focal point at point 1. Which picture shows the rays leaving the lens? Answer: D 12

Question 3 Light rays are converging to point 1. The lens is inserted into the rays with its focal point at point 1. Which picture shows the rays leaving the lens? Answer: D D. 13

Question 4 A lens creates an image as shown. In this situation, s < f f < s < 2f s > 2f There’s not enough information to compare s to f Answer: B 14

Question 4 A lens creates an image as shown. In this situation, s < f f < s < 2f s > 2f There’s not enough information to compare s to f The image is real, which requires s > f. The image is taller than the object, and s > s requires s < 2f. Answer: B 15

Question 5 In this figure the image is produced by a lens. At which position is the lens? Answer: D

Question 5 In this figure the image is produced by a lens. At which position is the lens? Answer: D D.