Which one among the following is the correct focal length of a combination of lenses of power 2.5 D and -2.0 D?

CONCEPT:

Combination of Lenses and Focal Length

• The power of a lens (P) is the reciprocal of its focal length (f) in meters, given by the equation:

  P = 1/f

• When combining multiple lenses, the total power (P_total) of the combination is the sum of the individual powers:

  P_total = P₁ + P₂ + ... + P_n

• The focal length of the combination (f_total) can then be found using the equation:

  f_total = 1 / P_total

EXPLANATION:

• Calculate the total power of the combination:
  • P_total = P₁ + P₂
  • = +2.5 D + (-2.0 D)
  • = +0.5 D
• Calculate the focal length of the combination:
  • f_total = 1 / P_total
  • = 1 / +0.5 D
  • = +2.0 m

Therefore, the correct focal length of the combination of lenses is +2.0 m.