An object is placed at a distance of 40 cm from a combination of two thin lenses in contact. The combination forms a real and inverted image of the same size as the object. If the power of one of the lenses is +10 D , what is the power of the second lens?

Step-by-step solution

For a real and inverted image of the same size as the object, the linear magnification m = -1 . Using the magnification formula m = v u : -1 = v -40 cm v = +40 cm . Applying the lens formula for the combination: 1 F = 1 v - 1 u 1 F = 1 40 - 1 -40 = 2 40 = 1 20 cm ⁻¹ . The effective focal length of the combination is F = +20 cm = +0.2 m . The effective power of the combination is: P_ net = 1 F ( in m ) = 1 0.2 = +5 D . The effective power is the sum of the individual powers: P_ net = P₁ + P₂ +5 D = +10 D + P₂ P₂ = -