Keanu is 47 years old, and the amplitude of accommodation in his left eye is about one standard deviation above average for his age. From now on, we concentrate exclusively on his left eye. When Keanu's eye is unaided by vision correction, he can focus on objects about 40 cm in front of it, but not closer. The following plot may be useful in what follows:

1.1. Show that Keanu's eye's sphere correction is about +2.5 D. Use this result in later problems even if you don't successfully compute it.

1.2. Is Keanu's eye hyperopic, emmetropic, or myopic?

1.3. If Keanu's eye has a minimum power of 57.5 D, what is its lens-retina distance d ?

1.4. Suppose that an object is 30 cm in front of Keanu's eye, and suppose the eye is using its maximum power. Determine the location of the corresponding image through numerical computation, and sketch a corresponding ray diagram that includes the object, the lens of his eye, his retina, the image, and appropriate rays that identify the location of the image. The ray diagram doesn't need to be to scale. Discuss how your calculations and ray diagram are consistent with the statement "he can see objects about 40 cm in front of it, but no closer" from the prior description of his vision.

1.5. Keanu wears a contact lens to correct his vision. The radius of curvature of the back surface of the contact is 8.8 mm. If the contact lens has an index of refraction of 1.65, what is the radius of curvature of its front surface in millimeters? Both the front and back surfaces are curved in the same direction as the cornea (bulging out away from the eye).

1.6. What is Keanu's far point distance (i) without vision correction and (ii) with vision correction?

1.7. What is Keanu's near point distance (i) without vision correction and (ii) with vision correction?

1.8. Consider the near point distance of Keanu's corrected vision. Suppose that we place an object at precisely that distance in front of his corrective contact lens without placing it on his eye (i.e. we're just considering how only the contact will affect light rays that enter it). Where would the corresponding image be? Determine the answer both numerically and independently using a ray diagram and ray tracing rules. Based where the contact lens makes it seem like light is coming from, explain how it makes sense that this lens enables Keanu to see objects closer than without the contact lens.