Item 14 Part A A lensmaker wants to make a magnifying glass from glass with n = 1.55 and with a focal length of 22.5 cm . If the two surfaces of the lens are to have equal radii, what should that radius be? Express your answer with the appropriate units. HA ? R = Value Units Submit Previous Answers Request AnswerItem 13 ( 130f14 > I Review | Constants V PartA In a two-lens system, the image produced by one lens acts as the object for the next lens. This simple principle tinds applications in many optical instruments, including some of common use such as the microscope and the telescope The microscope available in your biology lab has a converging lens (the eyepiece) with a focal length of 2.50 cm mounted on one end at a tube of adjustable length. At the other end is another converging lens (the objective) that has a focal length of 1.00 cm . When you place the sample to be examined at a distance of 1.30 cm from the objective, at what length I will you need to adjust the tube of the microscope in order to view the sample in focus with a completely relaxed eye? Note that to view the sample with a completely relaxed eye, the eyepiece must form its image at infinity. The length I here is the distance between the eyepiece and objective lens. Express your answer in centimeters. ? View Available Hint(s) Ammo? 1: cm Item 12 12 of 14 Review | Constants Part A A compound lens system consists of two converging lenses, one at * = -20.0 cm with focal length f1 = +10.0 cm, and the other at x = +20.0 cm with focal length f2 = +8.00 cm. (Figure 1)An What is the location of the final image produced by the compound lens system? Give the x coordinate of the image. object 1.00 centimeter tall is placed at x = -50.0 cm. Express your answer in centimeters, to three significant figures or as a fraction. View Available Hint(s) AZO c = cm Submit Part B Complete previous part(s) Part C Complete previous part(s) Now remove the two lenses at x = +20.0 cm and x = -20.0 cm and replace them with a single lens of focal length f at x = 0. We want to choose this new lens so that it produces an image at the same location as before. Part D What is the focal length of the new lens at the origin? Express your answer in centimeters, to three significant figures or as a fraction. View Available Hint(s) AEd 10 2 ? f3 = cm SubmitItem 11 I Review | Constants V PartA A person with normal vision can focus on objects as close as a few centimeters from the eye up to objects infinitely far away. There exist, however, certain conditions under which the range of vision is not so extendedt For example, a nearsighted person cannot focus on objects farther than a certain point (the far point), while a farsighted person cannot focus on objects closer than a certain point (the near point)' Note that even though the presence of a near point is common to everyone, a farsighted person has a near point that is much farther from the eye than the near point of a person with normal vision. Both nearsightedness and farsightedness can be corrected with the use of glasses or contact lenses. In this case, the eye converges the light coming from the image formed by the corrective lens rather than from the object itself. When glasses (or contact lenses) are used to correct nearsightedness, where should the corrective lens form an image of an object located at infinity in order for the eye to form a clear image of that object? b View Available Hint(s) O The lens should form the image at the near point. 0 The lens should form the image at the far point. 0 The lens should form the image at a point closer to the eye than the near point. 0 The lens should form the image at a point farther from the eye than the far point. Part B Complete previous part(s) V PartC When glasses (or contact lenses) are used to correct farsightedness. where should the corrective lens form an image of an object located between the eye and the near point in order for the eye to form a clear image of that object? F View Available Hint(s) O The lens should form the image at the near point. 0 The lens should form the image at the far point. 0 The lens should form the image at a point closer to the eye than the near point. 0 The lens should form the image at a point farther from the eye than the far point. Item 10 Now let's apply the thin-lens equation to a diverging lens. and then we will conlirm our results by constructing the image using a ray diagram. Suppose that you are given a thin diverging lens and you lind that a beam of parallel rays spreads out after passing through the lens, as though all the rays came from a point 20.0 cm from the center of the lens. You want to use this lens to [arm an upright, virtual image that is one-third the height of a real object. (8) Where should the object be placed? (b) Draw a principal-ray diagram. SOLUTION SET UP AND SOLVE Part (a): The behavior oi the parallel incident rays indicates that the focal length is negative: f : 20.0 cm. We want the lateral magnication to be m = +1/3 (positive because the image is to be upright). From the definition of magnification. m = 1/3 = s '/3. So we use 3 ' = s/3 in the thin lens equation: 1 + 1 1 s s' f 1 + 1 1 3 is / 3 20.0 cm s 40.0 cm 40.0 cm 5' T : 13.3 cm Part ([7): (gure 1 shows our principal-ray diagram [or this problem. REFLECT In part (a), the image distance is negative, so the real object and the virtual image are on the same side of the lens. V Part A- Practice Problem: