To determine the power of the lens combination prescribed by the eye specialist, we need to consider the individual powers of the convex and concave lenses and their combination.



The power of a lens is a measure of its ability to converge or diverge light. It is given by the formula:

Power (P) = 1 / F

Where F is the focal length of the lens measured in meters.



The convex lens prescribed by the eye specialist has a focal length of 40 cm. To calculate its power, we convert the focal length from centimeters to meters:

Focal length (F) = 40 cm = 0.4 m

Therefore, the power of the convex lens is:

Power (P1) = 1 / 0.4 = 2.5 diopters (D)



The concave lens in contact with the convex lens has a focal length of 25 cm. Again, we convert the focal length to meters to calculate its power:

Focal length (F) = 25 cm = 0.25 m

The power of the concave lens is:

Power (P2) = 1 / 0.25 = -4 diopters (D)

Note that the power of a concave lens is negative as it diverges light.



To determine the power of the lens combination, we add the powers of the individual lenses:

Power (P) = P1 + P2

P = 2.5 D + (-4 D)

P = -1.5 D

Therefore, the power of the lens combination prescribed by the eye specialist is -1.5 diopters (D).



The combination of a convex lens and a concave lens allows for the correction of certain eye conditions, such as myopia (nearsightedness) or hyperopia (farsightedness). By combining lenses with different powers, the eye specialist can effectively adjust the overall power of the lens system to correct the refractive error.

In this case, the convex lens has a positive power of +2.5 D, which helps in converging the light rays. The concave lens, with a negative power of -4 D, diverges the light rays. When these lenses are placed in contact, the overall power of the lens system is determined by the algebraic sum of their individual powers.

The negative power of -1.5 D indicates that the lens combination corrects a refractive error, such as myopia, where the light rays converge in front of the retina. The lens combination helps to shift the focus of the light rays onto the retina, improving vision for the individual.