33. Geometric Optics

A converging lens with a focal length of 9.00 cm forms an of a 4.00-mm-tall real object that is to the left of the lens. The is 1.30 cm tall and erect. Where are the object and located? Is the real or virtual?

A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

For each thin lens shown in Fig. E34.37, calculate the location of the of an object that is 18.0 cm to the left of the lens. The lens material has a refractive index of 1.50, and the radii of curvature shown are only the magnitudes. (b)

An object is 16.0 cm to the left of a lens. The lens forms an 36.0 cm to the right of the lens. (b) If the object is 8.00 mm tall, how tall is the ? Is it erect or inverted?

You wish to project the of a slide on a screen 9.00 m from the lens of a slide projector. (b) If the dimensions of the picture on a 35-mm color slide are 24 mm * 36 mm, what is the minimum size of the projector screen required to accommodate the ?

Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (b) The of the converging lens serves as the object for the diverging lens. What is the object distance for the diverging lens? (c) Where is the final ? Compare your answer to Fig. 34.43a.

A camera lens has a focal length of 180.0 mm and an aperture diameter of 16.36 mm. (a) What is the ƒ-number of the lens?

A 25-cm-long rod lies along the optical axis of a converging lens, perpendicular to the lens plane. The lens has a 30 cm focal length. The rod's real , along the optical axis on the other side of the lens, is also 25 cm long. What is the distance from the lens to the nearest end of the rod?

FIGURE CP35.50 shows a lens combination in which the lens separation is less than the focal length of the converging lens. The procedure for combination lenses is to let the of the first lens be the object for the second lens, but in this case the of the first lens—shown as a dot—is on the far side of the second lens. This is called a virtual object, a point that light rays are converging toward but never reach. The top half of Figure CP35.50 shows that the converging rays are refracted again by the diverging lens and come to a focus farther to the right. The procedure for combination lenses will continue to work if we use a negative object distance for a virtual object.b. Equation 35.1 defined the effective focal length fₑբբ of a lens combination, but we didn't discuss how it is used. Although an actual ray refracts twice, once at each lens, we can extend the output rays leftward to where they need to bend only once in a plane called the principal plane. The principal plane is similar to the lens plane of a single lens, where a single bend occurs, but the principal plane generally does not coincide with the physical lens; it's just a mathematical plane in space. The effective focal length is measured from the principal plane, so parallel input rays are focused at distance fₑբբ beyond the principal plane. Find the positions of the principal planes for lens separations of 5 cm and 10 cm. Give your answers as distances to the left of the diverging lens.