33. Geometric Optics

If an object is placed within the focus of a converging lens (it's at a distance of less than the focal length), will a real image form? If so, does it form at a distance less than or greater than the focal length?

If an object is placed within the focus of a diverging lens (it's at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

If an object is placed within the focus of a converging lens (it's at a distance of less than the focal length), will a real image form? If so, does it form at a distance less than or greater than the focal length?

If an object is placed within the focus of a diverging lens (it's at a distance of less than the focal length), where will the image form? If so, does it form at a distance less than or greater than the focal length?

(I) (a) What is the power of a 26.5-cm-focal-length lens? (b) What is the focal length of a -6.25 -D lens? Are these lenses converging or diverging?

(II) A 105-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 132 mm. (a) How far in front of the sensor should the lens (assumed thin) be positioned if the object to be photographed is 10.0 m away? (b) 3.0 m away? (c) 1.0 m away? (d) What is the closest object this lens could photograph sharply?

(I) A sharp image is located 373 mm behind a 235-mm-focal-length converging lens. Find the object distance (b) by calculation.

(II) It is desired to magnify reading material by a factor of 3.0 x when a book is placed 9.0 cm behind a lens. (a) Draw a ray diagram and describe the type of image this would be. (b) What type of lens is needed? (c) What is the power of the lens in diopters?

(II) Two 28.0-cm-focal-length converging lenses are placed 16.5 cm apart. An object is placed 35.0 cm in front of one lens. (a) Where will the final image formed by the second lens be located? (b) What is the total magnification?

Both a converging lens and a concave mirror can produce virtual images that are larger than the object. Concave mirrors can be used as magnifying makeup or shaving mirrors, but converging lenses cannot be. (a) Draw ray diagrams to explain why not. (b) If a concave mirror has the same focal length as a converging lens, and an object is placed first at a distance of 1/2ƒ from the lens and then at a distance of 1/2ƒ from the mirror, how will the magnification of the object compare in the two cases?