To determine the type and focal length of a lens that has the same power as the combination of a thin converging lens and a thin diverging lens, we can use the lensmaker's formula for thin lenses:
1/f_total = 1/f_converging - 1/f_diverging
where f_total is the focal length of the combined lenses, f_converging is the focal length of the converging lens, and f_diverging is the focal length of the diverging lens.
Given that f_converging = 6 cm and f_diverging = 8 cm, we can calculate the total focal length (f_total):
1/f_total = 1/6 - 1/8
1/f_total = (4 - 3) / 24
1/f_total = 1 / 24
Now, to find the total focal length (f_total), we take the reciprocal of both sides:
f_total = 24 cm
Now that we have the total focal length (f_total), we can determine the type of lens based on the sign of f_total:
- If f_total is positive, it is a converging lens.
- If f_total is negative, it is a diverging lens.
In this case, f_total is positive (24 cm), so the lens that has the same power as the combination of the given lenses is a **converging lens with a focal length of 24 cm**.