To find the focal length of a compound lens, we can use the formula:

1/f = (n - 1) [(1/r1) - (1/r2)]

where f is the focal length of the lens, n is the refractive index of the lens material, and r1 and r2 are the radii of curvature of the lens surfaces.



For the first lens with power 12.5D, we can use the formula:

P = 1/f

where P is the power of the lens and f is the focal length. Rearranging this formula, we get:

f = 1/P

Substituting P = 12.5D, we get:

f1 = 1/12.5 = 0.08m

Similarly, for the second lens with power -2.5D, we get:

f2 = -1/(-2.5) = 0.4m

(Note: The negative sign indicates that the lens is a diverging lens.)



To calculate the focal length of the compound lens, we can use the formula:

1/f = 1/f1 + 1/f2

Substituting the values of f1 and f2, we get:

1/f = 1/0.08 + 1/0.4 = 15

Therefore, the focal length of the compound lens is:

f = 1/15 = 0.067m



To calculate the power of the compound lens, we can use the formula:

P = 1/f

Substituting the value of f, we get:

P = 1/0.067 = 14.93D

Therefore, the power of the compound lens is:

P = 14.93D

(Note: The power is positive, indicating that the compound lens is a converging lens.)



In conclusion, a compound lens made up of two lenses with powers 12.5D and -2.5D has a focal length of 0.067m and a power of 14.93D. The first lens has a focal length of 0.08m, while the second lens has a focal length of 0.4m. The power of the compound lens is positive, indicating that it is a converging lens.