An object is placed against the center of a thin lens and then moved 72 cm from it along the central axis as the image distance i is measured. The figure gives | versus object distance p out to p; = 48 cm. What is the image distance when p = 72 cm? 0 fricm) i {em) Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is p. = +25 cm, the type of mirror is convex, and then the distance between the focal point and the mirror is 50 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (a) MNumber n n Units cm - (b) Number n n Units cm e @ v D .- (e) noninverted (f) opposite v In the figure, a real inverted image | of an object O is formed by a certain lens (not shown); the object-image separationis d = 42.4 cm, measured along the central axis of the lens. The image is just 1/5 the size of the object. (a) What kind of lens must be used to produce this image? (b) How far from the object must the lens be placed? (c) What is the focal length of the lens? Lenses with given radii. Object O stands in front of a thin lens, on the central axis. For this situation, each problem in the table (below) gives object distance p, index of refraction n of the lens, radius r of the nearer lens surface, and radius ry of the farther lens surface. (All distances are in centimeters.) Find (a) the image distance i and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of the lens as object O or on the opposite side. (a) (b) (c) (d) (e) p n r1 r2 i m R/V 1/NI Side +17 1.7 -28 +23 (a) Number Units (b) Number Units (c) (d) (e)Spherical refracting surfaces. An object O stands on the central axis of a spherical refracting surface. For this situation (see the table below, all distances are in centimeters), my is the index of refraction where the object is located, n2 is the index of refraction on the other side of the refracting surface. Find (a) the image distance i, and determine whether the image is (b) real or virtual and (c) on the same side of the surface as object O or on the opposite side. (a) (b) (c) n1 02 P r i R/V Side 1.9 1.4 +84 +45 (a) Number Units (b) virtual (c) sameSpherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is p. = +24 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 32 em (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance J, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side. (b) Number n n Units cm v 0