Unless otherwise stated, the lens-to-retina distance is 2.00 cm.

(a) A laser vision correction reshaping the cornea of a myopic patient reduces the power of his eye by 9.00 D, with a$\mathbf{\pm }\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{\%}$uncertainty in the final correction. What is the range of dioptres for spectacle lenses that this person might need after LASIK procedure? (b) Was the person near-sighted or farsighted before the procedure? How do you know?

The ability of a lens to bend the light falling on it is called the power of a lens. Since the lens of a shorter focal length will bend the light rays, more will have more power. A convex lens converges the light rays towards the principal axis whereas a concave lens diverges the light rays away from the principal axis.

Since the power of the cornea is required to decrease by 9.00 D, and the uncertainty of the user device to obtain the required decrease in power is within$\pm 5\%$ uncertainty, this means that the final decrease of the error is thus,

$9.00\pm \left(\frac{9.00\times 5.00\%}{100}\right)$

This means, that the achieved decrease in the cornea's power can range from 8.55 D to 9.45 D.

Since the required decrease in the cornea's power for the patient to have a normal vision is 9.00 D, this means that he might need a correction spectacle which ranges in the value of error, that means $\pm 0.45D$.

If the correction was less than the required correction value (i.e., the power of the cornea decreased by 8.55 D only, the lens works on decreasing the total eye power even more), to +0.45 D if the cornea was over-corrected (i.e., the cornea's power has decreased by 9.45 D, the lens works in increasing the total power of the eye).

Therefore, the range of the spectacle’s lenses power, which the patient might need after the laser vision correction is thus,

-0.45 D to +0.45 D

Therefore, the range of dioptres is obtained as -0.45 D to +0.45 D.

Since the total power of the eye needs to be decreased, this means that the eye was converging that light ray coming into the eye too strong, such that incoming light ray gets converged in front of the retina, i.e., this is a condition of myopia (Near-sightedness).

Therefore, the person was having near-sightedness.