When two thin lenses are placed in contact, they act like a single lens. The power of the combination is the sum of the individual powers:P = P1 + P2 This is one reason power is useful: powers simply add, whereas focal lengths do not. To find the combined focal length, add the powers first and then use f = 1/P.Remember the signs. Converging lenses have positive power and diverging lenses negative power, so a diverging lens reduces the total power.Worked example 1: lenses of +5.0 D and +3.0 D are placed together.
P = 5.0 + 3.0 = +8.0 D, so f = 1 / 8.0 = 0.125 m (12.5 cm).Worked example 2: a converging lens of +10 D is placed in contact with a diverging lens of −4.0 D.
P = 10 + (−4.0) = +6.0 D, so f = 1 / 6.0 = 0.17 m. The combination is still converging, but weaker.Worked example 3: two converging lenses have focal lengths 0.20 m and 0.50 m. Their powers are 5.0 D and 2.0 D, so P = 7.0 D and f = 1 / 7.0 = 0.14 m. Note that simply adding the focal lengths (0.70 m) would be wrong.Combinations of lenses are used in camera lenses and microscopes. Pairing a converging and a diverging lens made of different glasses can reduce chromatic aberration. When you wear glasses, the power of the spectacle lens adds to the power of your eye.
P = 5.0 + 3.0 = +8.0 D, so f = 1 / 8.0 = 0.125 m (12.5 cm).Worked example 2: a converging lens of +10 D is placed in contact with a diverging lens of −4.0 D.
P = 10 + (−4.0) = +6.0 D, so f = 1 / 6.0 = 0.17 m. The combination is still converging, but weaker.Worked example 3: two converging lenses have focal lengths 0.20 m and 0.50 m. Their powers are 5.0 D and 2.0 D, so P = 7.0 D and f = 1 / 7.0 = 0.14 m. Note that simply adding the focal lengths (0.70 m) would be wrong.Combinations of lenses are used in camera lenses and microscopes. Pairing a converging and a diverging lens made of different glasses can reduce chromatic aberration. When you wear glasses, the power of the spectacle lens adds to the power of your eye.