To fit a contact lens to a patient's eye, a keratometer can be used to measure the curvature of the cornea—the front surface of the eye. This instrument places an illuminated object of known size at a known distance p from the cornea, which then reflects some light from the object, forming an image of it. The magnification M of the image is measured by using a small viewing telescope that allows a comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea when p = 34.0 cm and M = 0.0160.

A lens system consists of a +4D lens and a +3D lens separated by 10 cm. Find the equivalent focal power and the positions of the principal points. An object 3 cm long is situated 50 cm in front of the first lens. What will be the position and size of the image produced by the combination?

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

Q1 a) The eyepiece of a refracting telescope has a focal length of 9.00cm. The distance between objective and eyepiece is 1.80m, and the final image is at infinity. What is the angular magnification of the telescope? F=580×10² 14

To fit a contact lens to a patient's eye, a keratometer can be used to measure the curvature of the cornea-the front surface of the eye. This instrument places an illuminated object of known size at a known distance p from the cornea, which then reflects some light from the object, forming an image of it. The magnification M of the image is measured by using a small viewing telescope that allows a comparison of the image formed by the cornea with a second calibrated image projected into the field of view by a prism arrangement. Determine the radius of curvature of the cornea whenp = 28.0 cm and M = 0.0140.

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.