Lens and mirror combination problems pdf

Physics Problem

Physics 103, Waves and Modern Physics

Prof. Haroyan

1. A plane mirror is 10 m away from and parallel to a second plane mirror. Find the location of the first five images formed by each mirror when an object is positioned 3 m from one of the mirrors?

Ans:

2. The opposite walls of a barber shop are covered by plane mirrors, so that multiple images arise from multiple reflections, and you see many reflected images of yourself, receding to infinity. The width of the shop 6.50 m, and you are standing 2.00m from the north wall. (a) How far apart are the first two images of you behind the north wall? (b) What is the separation of the first two images of you behind the south wall? Explain your answer.

Ans:

3. The radius of curvature of a spherical concave mirror is 20 cm. De- scribe the image formed when a 10cm tall object is positioned (a) 5 cm from the mirror, (b) 20 cm from the mirror, (c) 50 cm from the mirror, and (d) 100 cm from the mirror. For each case give the image distance, the image height, the type of image (real or virtual), the orientation of the image (upright or inverted) and the ray diagram.

Ans:

4. A car’s convex rear view mirror has a radius of curvature equal to 15m. What are the magnification, type, and location of the image

1

that is formed by an object that is 10 m from the mirror?

Ans:

5. Using the mirror equation, prove that all images in spherical convex mirrors are virtual.

Ans:

6. A typical person’s eye is 2.5 cm in diameter and has a near point (the closest an object can be and still be seen in focus) of 25 cm, and a far point (the farthest an object can be and still be in focus) of infinity. What is the range of the effective focal lengths of the focusing mechanism (lens plus cornea) of the typical eye? (b) Is the equivalent focusing mechanism of the eye a diverging or a con- verging lens? Justify your answer without using any mathematics, and then see if your answer is consistent with your result in part (a).

Ans:

7. A geneticist looks through a microscope to determine the phenotype of a fruit fly. The microscope is set to an overall magnification of 400 x with an objective lens that has a focal length of 0.60 cm. The distance between the eyepiece and objective lenses is 16 cm. Find the focal length of the eyepiece lens assuming a near point of 25 cm (the closest an object can be and still be seen in focus). Ans:

8. You are designing lenses that consist of small double convex pieces of plastic having surfaces with radii of curvature of magnitudes 3.50cm on one side and 4.25 cm on the other side. You want the lenses to have a focal length of 1.65 cm in air. What should be the index of

2

refraction of the plastic to achieve the desired focal length? Ans:

9. A thin, plano-concave lens having a focal length of magnitude 45.0 cm has the same principal axis as a concave mirror with a radius of 60.0cm. The center of the mirror is 20.0 cm from the lens, with the lens in front of the mirror. An object is placed 15.0 cm in front of the lens. (a) Where is the final image due to the lens-mirror combination? (b) Is the final image real or virtual? Upright or inverted? (c) Suppose now that the concave mirror is replaced by a convex mirror of the same radius. Repeat parts (a) and (b) for the new lens-mirror combination. Ans:

10. Using the lens maker’s equation, find the radius of curvature needed for the leading surface (in other words, R1 =?) to optimize the power of the lens. Assume that the secondary surface has a fixed radius of curvature, R2 Hint: Write the power (P) as a function of R1, and apply the maximization condition. Yes, you need to use calculus. Ans:

11. A nearsighted eye is corrected by placing a diverging lens in front of the eye. The lens will create a virtual image of a distant object at the far point (the farthest an object can be and still be in focus) of the myopic viewer where it will be clearly seen. In the traditional treatment of myopia, an object at infinity is focused to the far point of the eye. If an individual has a far point of 70 cm, prescribe the correct power of the lens that is needed. Ans:

12. A farsighted eye is corrected by placing a converging lens in front of the eye. The lens will create a virtual image that is located at the

3

near point (the closest an object can be and still be in focus) of the viewer when the object is held at a comfortable distance (usually taken to be 25 cm). If a person has a near point of 75 cm, what power reading glasses should be prescribed to treat this hyperopia? Ans:

13. An optometrist tests a person and finds that without glasses, he needs to have his eyes 15.0 cm from a book to read comfortably and can focus clearly only on distant objects up to 2.75 m away, but no farther. A typical normal eye should be able to focus on objects that are between 25.0 cm (the near point) and infinity (the far point) from the eye. (a) What type of correcting lenses does the person need: single focal length or bifocals? Why? (b) What should the optometrist specify as the focal length of the correcting contact lens or lenses? (c)What is the power (in diopters) of the correcting lens or lenses? Ans:

14. A common zoom lens for a digital camera covers a focal length range of 18 mm to 200 mm. For the purposes of this problem, treat the lens as a thin lens. If the lens is zoomed out to 200 mm and is focused on a petroglyph that is 15.0 m away and 38 cm wide, (a) how far is the lens from the photosensor array of the camera and (b) how wide is the image of the petroglyph on the sensors? (c) If the closest that the lens can get to the sensors at its 18 mm focal length is 5.2 cm, what is the closest object it can focus on at that focal length Ans: