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An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths f1 = -28.1 cm and f2 = 25.3 cm .

(a) is the combination converging or diverging?

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Final answer:

The combination of a diverging lens with focal length -28.1 cm and a converging lens with focal length 25.3 cm has a positive net focal length, indicating that the combination acts as a converging lens.

Step-by-step explanation:

The student has asked about an achromatic lens which is made by combining two thin lenses with focal lengths f1 = -28.1 cm (a diverging lens) and f2 = 25.3 cm (a converging lens). To determine whether the combination is converging or diverging, one can calculate the net focal length of the system.

Using the lensmaker's equation for thin lenses in contact, the net focal length F is given by the reciprocal of the algebraic sum of the reciprocals of the individual focal lengths:

1/F = 1/f1 + 1/f2

Substituting the given values:

1/F = 1/(-28.1) + 1/(25.3)

1/F = -0.0356 + 0.0395 = 0.0039

Therefore, F ≈ 256.4 cm. Since the net focal length is positive, the combination of the two lenses acts as a converging lens.

Moreover, the combination is used to correct chromatic aberration, which is a common problem in single lenses where different wavelengths of light are focused at different points. An achromatic lens uses lenses made of different materials to focus all colors at the same point and thus, provide a clearer image.

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