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determine the type and focal length of a lens that has the same power as a combination of a thin converging lens of focal length 6cm and a thin diverging lens of focal length 8cm​

User Dbader
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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**.

User Louzoid
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