Final answer:
The correct method to determine the combined focal length of one concave and one convex lens separated by a distance is to use the lens formula with appropriate signs, considering the power of each lens and the distance between them. Option C is the correct answer.
Step-by-step explanation:
To determine the combined focal length of one concave and one convex lens separated by a finite distance, we cannot simply add or subtract the individual focal lengths. Instead, we must consider the power of each lens and use the lens formula with appropriate signs. The power of a lens, which is the inverse of the focal length (P = 1/f), is measured in diopters (D). For convex lenses, the focal length is positive, and for concave lenses, it is negative.
The total power of two lenses in contact (Ptotal) is the sum of their individual powers (P1 + P2). The total focal length (ftotal) can then be calculated as the inverse of the total power (ftotal = 1/Ptotal). However, when lenses are not in direct contact, but separated by a distance (d), we must also account for this separation in our calculations. The effective focal length (feff) of two thin lenses separated by a distance (d) is given by the formula:
1/feff = 1/f1 + 1/f2 - d/(f1 × f2)
In this formula, f1 is the focal length of the first lens, f2 is the focal length of the second lens, and d is the distance between the lenses. By applying this formula, the combined effect of the two lenses on light passing through them can be found, yielding the effective focal length of the system. Therefore, the correct option is C. Use the lens formula with appropriate signs.