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Optical Power of Lenses: Understanding and Calculations

Learn about optical power in lenses, its relation to focal length, types of lenses, and how to calculate optical power and focal lengths. Practice exercises included.

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Optical Power of Lenses: Understanding and Calculations

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  1. High School PHYSICS InClass by SSL Technologies with S. Lancione Exercise-54 Optical Power

  2. Optical Power The optical power of a lens is a measure of how much the lens bends light. The greater the optical power, the more the lens bends light. Note that the optical power is the reciprocal of the focal length of the lens. The symbol for the optical power of a lens is P and the unit for the optical power is dioptres and is designated by the Greek symbol “”. More bending Less bending High optical power Low optical power Click

  3. Optical Power The optical power of a lens is the reciprocal of its focal length. Study these examples: f = 1 cm P = 1/0.01 m = 100 f = 2 cm P = 1/0.02 m = 50  f = 4 cm P = 1/0.04 m = 25  f = 8 cm P = 1/0.08 m = 12.5  f = 10 cm P = 1/0.1 m = 10  f = 25 cm P = 1/0.25 m = 4  f = 50 cm P = 1/0.50 m = 2  f = 100 cm P = 1/1 m = 1  Note that the optical power of a converging lensis positive and for a diverging lens it is negative. Click

  4. REMEMBER Remember this! The optical power of a convex (or converging) lens is positive. The optical power of a concave (or diverging) lens is negative. Click delay

  5. Optical Power Two or more lenses may be combined to form a compound lensor an optical system. For such a compound lens, the total optical power is given by the following formula: Click

  6. EXERCISES

  7. Question-1 Define the optical power of a lens. The ability of a lens to bend (converge or diverge) light rays. Click

  8. Question-2 What type of a lens has positive optical power? Converging lens. Click

  9. Question-3 What type of a lens has a negative optical power? Diverging lens. Click

  10. Question-4 Listed below are the focal lengths of five lenses. Determine their optical powers. a) f = 1 cm Click

  11. Question-4 Listed below are the focal lengths of five lenses. Determine their optical powers. b) f = 5 cm Click

  12. Question-4 Listed below are the focal lengths of five lenses. Determine their optical powers. c) f = 10 cm Click

  13. Question-4 Note that the negative sign indicates a diverging lens. Listed below are the focal lengths of five lenses. Determine their optical powers. d) f = -20 cm Click

  14. Question-4 Listed below are the focal lengths of five lenses. Determine their optical powers. e) f = 15 cm Click

  15. Question-5 Listed below are the optical powers of four lenses. Determine their focal lengths. a) P = 20  Click

  16. Question-5 Listed below are the optical powers of four lenses. Determine their focal lengths. b) P = 10  Click

  17. Question-5 Listed below are the optical powers of four lenses. Determine their focal lengths. c) P = -25  Note that the negative sign indicates a diverging lens. Click

  18. Question-5 Listed below are the optical powers of four lenses. Determine their focal lengths. d) P = 8  Click

  19. Question-6 A converging lens has a focal length of 25 cm. Determine its optical power. Click

  20. Question-7 Note that diverging lens has a negative optical power. The optical power of a diverging lens is – 8.33 . Determine its focal length. Click

  21. Question-8 Draw the rays emerging from a lens having the following opticalpowers: 5 cm a) P = 20  Click

  22. Question-8 Draw the rays emerging from a lens having the following opticalpowers: 25 cm b) P = 4  Click

  23. Question-8 Draw the rays emerging from a lens having the following opticalpowers: c) P = -20  5 cm REMINDER By convention in using lenses,distances are positive on theside where light comes out. F Click

  24. Question-8 Draw the rays emerging from a lens having the following opticalpowers: d) P = -4  25 cm F Click

  25. Question-9 Two thin lenses are placed together to form an effective lens system. The lenses have optical powers of 20.0  and –12.0 respectively. Find the focal length of the system. Click

  26. Question-10 The negative sign indicatesthe system is acting as a diverging (concave) lens. A lens system consists of a converging lens and a diverging lens. The focal length of the converging lens is 60 cm. If the optical power of the system is to be 1.25 ,what should be the focal length of the diverging lens? Click

  27. Question-11 Convert to metres An optical system is made using two thin lenses placed close toeach other. The optical power of the system is 4 δ (dioptres). Knowing that one of the lenses has a focal length of -16 cm,determine the optical power of the second lens. REMINDERThe unit for length in the optical power formula must be metres. A) 13.5 δ B) 10.3 δ C) 9.6 δ D) 3.4 δ E) -2.9 δ Click

  28. Question-12 Convert to metres. Three lenses have focal lengths of 10.5 cm, -7.5 cm and 5 cmrespectively. The lenses are combined to form an optical system. Determine the optical power of this lens system. A) 0.08 δ B) 0.23 δ C) 2.70 δ D) 16 δ E) 43 δ Click

  29. Question-13 120 cm Object Negative sign indicates inversion Two lenses are placed together to forman optical system. One lens has afocal length of 20.0 cm while the otherlens has a focal length of -35.0 cm. If an object 4.0 cm tall is placed 120 cm in front of thesystem determine the characteristics of the image. Given Calculation of fT Calculation of di Calculation of hi Click

  30. Question-14 Convert 25 cm to meters The focal length of a lens system is 25 cm. What is the optical power of this system? A) 4.0  B) -4.0  C) 0.04  D) -0.04  E) 0.25  Click

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