In an alternate universe, you are a brilliant optician. A young Harry Potter comes to you for a diagnosis. Alas, you find he has hyperopia. You measure his near point to be 1.5m from his eyes. Determine the power of the eyeglasses that will allow him to see nearby objects up to 25cm from his eye clearly if the eyeglasses will be 0.9cm in front of his eyes.

An office administrator realizes that she is having trouble doing her work due to eyesight problems. Her optometrist determines that without glasses she can focus clearly only on objects that lie at distances between 0.450 m and 4.00 m. The optometrist decides that the best way to handle her eyesight problems is to prescribe bifocals that will give her normal visual acuity from 25.0 cm out to infinity. After trying on several pairs of glasses frames, they agree that the glasses will be a distance of 2.20 cm from her eyes. (a) Determine the refractive power needed for the bifocal part that will correct for her nearsightedness (include the sign). D What type of lens is needed? O converging O diverging (b) Determine the refractive power needed for the bifocal part that will correct for her farsightedness (include the sign). D What type of lens is needed? O converging diverging

A laser beam of diameter d₁-1.1 mm is directed along the optical axis of a thin lens of focal length +4.7 cm (see figure below). (a) How far from the lens will the beam be focused? (b) A second positive lens is placed to the right of the first. Light emerges from the second lens in a parallel beam of diameter dy 3.6 mm. Thus the combination of lenses acts as a beam expander. Find the focal length of the second lens. Find the distance between the lenses.

A laser beam of diameter d1 = 1.3 mm is directed along the optical axis of a thin lens of focal length +5.1 cm (see figure below).   (a) How far from the lens will the beam be focused?(b) A second positive lens is placed to the right of the first. Light emerges from the second lens in a parallel beam of diameter d2 = 3.9 mm. Thus the combination of lenses acts as a beam expander. Find the focal length of the second lens.Find the distance between the lenses.