If you view a person through a negative lens (diverging), they appear much smaller than they actually are. This particular ens has a focal length of -42.29 cm. Looking at your friend through the lens, their face appears to be 11.37 cm long and 24.30 cm behind the lens. Determine the following. (a) The actual distance of the person behind the lens. cm (b) The actual length of their face. cm
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- Two identical diverging lenses are separated by 18 cm. The focal length of each lens is -8.0 cm. An object is located 4.0 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right. cm(a) As shown in Fig. la, the object and the screen is separated by 1 = 100cm. When we put a convex lens in the middle point between the object and the screen, a clear image is formed on the screen. What is the focal length of the lens? You may use either ABCD matrix or other methods. 100cm Fig. la (b) Now we replace the lens in (a) with an unknown lens (focal length f), as shown in Fig. 1b. Assume the distance between the object and the lens is S cm, what is the ABCD matrix from the object to the screen? What can we know about this matrix if a clear image is formed on the screen? 100cm P1 20cm P2 Fig. 1b (c) When we move the lens back and forth, we find that there exist two positions (Pl and P2 as shown in Fig. 1b) where clear image can be formed on the screen. The separation between the two positions is measured to be 20 cm. Is the unknown lens convex or concave? What is the focal length? Hint: The solution of a quadratic equation ax +bx+c=0 is -b±yb² – 4ac 2aA converging lens has a focal length of 18.4 cm. Construct accurate ray diagrams for object distances of (1) 6.13 cm and (i) 92.0 cm. (a) From your ray diagrams, determine the location of each image. Image (1) distance 9.19 cm location in front of the lens Image (ii) distance 0.043 (b) Is the image (1) real or virtual? real o virtual cm location on the back side of the lens: Is the image (ii) real or virtual? o real virtual (c) Is the image (i) upright or inverted? o upright inverted Is the image (ii) upright or inverted? upright o inverted #✓ (d) What is the magnification of the image? Image (i) 1.5 Image (1) -0.000045 (e) Compare your results with the values found algebraically. This answer has not been graded yet. (f) Comment on difficulties in constructing the graph that could lead to differences between the graphical and algebraic answers.
- Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +21 centimeters, the type of mirror is convex, and then the distance between the focal point and the mirror is 14 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 typical human eye is nearly spherical, and is usually about 2.5 cm in diameter. Suppose a person first looks at a coin that is 2.4 cm in diameter and located 34.0 cm from her eye. Then, she looks up at a friend who is 1.8 m tall and 4.00 m away. Find the magnitude of the approximate size of each image (coin ℎI,coin and friend ℎI,friend) on her retina. (Hint: Just consider rays from the top and bottom of the object that pass through the center of the lens.) b) Are the images on her retina upright/inverted and/or virtual/real?Homework 12 Problem 10: Two lenses are mounted d = 27 cm apart on an optical bench. The focal length of the first lens is f1 = 5.1 cm and that of the second lens is f2 = 4.4 cm. An object of height ho = 3.5 cm is placed at a distance of do = 21 cm in front of the first lens. Part (a) Ignoring the second lens for now, at what distance, in centimeters, behind the first lens is the object’s image formed by that lens? di = ______ Part (b) Calculate the magnification of that image, including its sign. m = ______ Part (c) Now consider the two-lens system and the final image it forms, i.e., the image created by the second lens. What is the distance, in centimeters, between the object and its final image? D = ______
- 1. 2. 3. What is the focal length of -4.50 D lens? Where is the focal point in the above lens and is it in front of or behind the lens? Would the image in the above lens be real or virtual?Photographs at a scale of S are required to cover an area X - mi square. The camera has a focal length and focal plane dimensions of 9 * 9in . If endlap is 60% and sidelap 30\% how many photos will be required to cover the area for the data given below? ▾ Part A S = 1/6500 ; X = 8 f = 152.4mn Express your answer as an integer.5) An object is placed in front of a circular mirror with a radius of curvature of 8 cm. A virtual image is formed 10 cm from the mirror. If the object and mirror are kept at the same location, but the radius of curvature is changed such that after is it is changed, the image formed is the opposite orientation as the image of the first radius and the magnification is 2.6 times smaller (the second image is 2.6 times smaller than the first image), what does the radius of curvature need to be in cm?