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Lenses

Lenses. Thin Lens & Magnification Equations. Thin Lens Equation. We can mathematically determine where an image will be formed in relation to the optical centre using the thin lens equation. The Thin Lens Equation. 1 = 1 + 1 f d i d o. d o. Focal length f. F.

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Lenses

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  1. Lenses Thin Lens & Magnification Equations

  2. Thin Lens Equation We can mathematically determine where an image will be formed in relation to the optical centre using the thin lens equation.

  3. The Thin Lens Equation 1 = 1 + 1 f di do do Focal length f F 2F 2F’ F’ di Where: f represents the focal length do represents from the object to the lens di represents from the image to the lens

  4. Thin Lens Rules

  5. The Thin Lens Equation – Example 1 • A converging lens has a focal length of 17 cm. A candle is located 48 cm from the lens. What type of image will be formed, and where will it be located?

  6. example 1 (cont'd) G: f = d0 = U: di = ? 17 cm 48 cm

  7. example 1 1 = 1 + 1 f di do E: Rearrange equation: 1 = 1 - 1 di f d0

  8. example 1…almost there! S: 1 = 1 - 1 di 17 cm 48 cm 1 = 0.03799cm-1 di di = 1 / 0.03799cm-1 S: di = 26.327165 cm = 26 cm S: The image of the candle is real and will be about 26 cm from the lens (opposite the object).

  9. example – last step! Sketch the ray diagram for this problem.

  10. Example 2: Thin Lens Equation and Diverging Lenses • A diverging Lens has a focal length of 29 cm. A virtual image of a marble is located 13 cm in front of the lens. Where is the marble (the object) located? • Follow the same steps as before, but be careful with the signs! Refer to your RULES for sign conventions.

  11. Example 2: G: 1 = 1 - 1 d0 -29cm -13cm S: f = - 29 cm di = -13 cm d0 = ? 1 = 0.042444 cm-1 d0 S: U: d0 = 23.560456 cm = 24 cm E: 1 = 1 + 1 f do di S: The marble is located 24 cm from the lens on the same side as the image. 1 = 1 - 1 d0 f di

  12. Example 2: Ray Diagram Sketch • Sketch:

  13. Magnification Equation M = hi = - di ho do ho F 2F 2F’ F’ hi Where: M stands for magnification hi stands for height of the image ho stands for height of the object

  14. Magnification Signs and Measurements • Magnification (M) has no units • M is POSITIVE for an UPRIGHT image • M is NEGATIVE for an INVERTED image If M is…. Then the image is… • GREATER THAN 1 LARGER than the object • BETWEEN 0 AND 1 SMALLER than the object • EQUAL TO 1 SAME SIZE as the object

  15. Example 3: Finding the Magnification of a CONVERGING lens • A toy of height 8.4 cm is balanced in front of a converging lens. An inverted, real image of height 23 cm is noticed on the other side of the lens. What is the magnification of the lens? • Follow the same steps as ex 1 & 2 to solve the problem (just use the magnification equation)

  16. Example 3: G: h0 = 8.4 cm hi = -23 cm M = ? S: M = -23 cm 8.4 cm U: S: M = -2.738095238 = -2.7 E: M = hi ho S: The lens has a magnification of -2.7, which means the image is inverted.

  17. Sketch

  18. Example 4: Magnification of a Diverging Lens • A coin of height 2.4 cm is placed in front of a diverging lens. An upright, virtual image of height 1.7 cm is noticed on the same side of the lens as the coin. What is the magnification of the lens?

  19. Example 4: G: S: h0 = 2.4 cm hi = 1.7 cm M = ? M = 1.7 cm 2.4 cm U: S: M = 0.708333 = 0.71 E: M = hi ho S: The lens has a magnification of 0.71, which means the image is upright.

  20. Sketch

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