Final answer:
The effective power of the combination of a lens with focal length +20cm and another with focal length -30cm, when placed in contact, is 1.67 diopters.
Step-by-step explanation:
The question relates to the combination of two thin lenses and finding their effective power when placed together. According to the principles of optics, the power of a lens is the reciprocal of its focal length (measured in meters) and is expressed in diopters (D). When lenses are in contact, their effective power (Ptotal) is the sum of their individual powers (P1 + P2).
Firstly, the power of each lens is calculated:
- For the lens with a focal length of +20 cm (or +0.2 meters), the power, P1, is 1/0.2 m = 5 D.
- For the lens with a focal length of -30 cm (or -0.3 meters), the power, P2, is 1/-0.3 m = -3.33 D.
Now we can find the effective power by adding the powers of both lenses:
Ptotal = P1 + P2 = 5 D - 3.33 D = 1.67 D.
Therefore, the effective power of the combination of the two lenses is 1.67 diopters.