Exam 27: Magnetic Field and Magnetic Forces

Camera: A 35-mm camera equipped with a 95 mm focal length lens is used to photograph a tree that is 8.0 m tall. A 32 mm high image of the tree on the film is needed. The required distance, between the tree and the camera lens, to take the photograph is closest to

Spherical mirrors: The spherical side mirror on a car is convex and has a radius of curvature of 25 cm. Another car is following, 20 m behind the mirror. If the height of the car is 1.6 m, how tall is its image?

Thin lenses: A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

Magnifying glass: What is the focal length of a magnifying glass that produces an angular magnification of 7.0 x when used by a person with a near point at 28 cm?

Thin lenses: An object 1.25 cm tall is placed 100 cm in front of a convex lens with a focal length of magnitude 50 cm. A concave lens with a focal length of magnitude 20 cm is placed 90 cm beyond the first lens. Where is the final image located?

Dispersion: Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. The index of refraction of the prism material for blue light is 1.530, and for red light it is 1.525. What is the angle between the two emerging beams of light?

Camera: A camera lens has a focal length of 50.0 mm and an aperture setting of f/4.00. What is the aperture diameter of this lens?

Compound microscope: The eyepiece of a compound microscope has a focal length of 2.50 cm and the objective has a focal length of 1.60 cm. The two lenses are separated by 15.0 cm. The microscope is used by a person with normal eyes (near point at 25 cm). What is the angular magnification of the microscope?

Thin lenses: It is desired to project the image of an object four times its actual size using a lens of focal length 20 cm. How far from the lens should the object be placed?

Snell's law: A ray of light goes from one transparent material into another, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Spherical mirrors: Suppose you place your face in front of a concave mirror. Which one of the following statements is correct?

Total internal reflection: A glass plate whose index of refraction is 1.56 is immersed in a liquid. The surface of the glass is inclined at an angle of 42.0° with the vertical. A horizontal ray in the glass is incident on the interface. When the liquid is a certain alcohol, the incident ray arrives at the interface at the critical angle. What is the index of refraction of the alcohol?

Eyes: A person can read the newspaper when it is held at 60 cm from his eyes. What should the focal length of his contact lenses be to allow him to read the newspaper comfortably at a distance of 30 cm?

Total internal reflection: What is the critical angle for light traveling from crown glass (n = 1.52) into water (n = 1.33)?

Snell's law: A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O crosses the brine-oil interface at a point 0.60 m from the axis. The ray continues and emerges into the air above the oil. What is the angle that the ray in the air makes with the vertical?

Compound microscope: The focal lengths of the objective and the eyepiece of a microscope are 0.50 cm and 2.0 cm, respectively, and their separation adjusted for minimum eyestrain (with the final image at the viewer's far point) is 6.0 cm. The near point of the person using the microscope is 25 cm and the far point is infinity. (a) If the microscope is focused on a small object, what is the distance between the object and the objective lens? (b) If the microscope is focused on a small object, what is its final magnification?

Snell's law: A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)

Magnifying glass: A person having a near point of 25 cm and a far point at infinity uses a converging lens of focal length 5.0 cm as a magnifying glass. What is the magnification if the person's eye is relaxed (with the image at his far point)?

Total internal reflection: An optical fiber made of glass with an index of refraction 1.50 is coated with a plastic with index of refraction 1.30. What is the critical angle of this fiber at the glass-plastic interface?

Lens-maker's formula: A double-concave lens has equal radii of curvature of An object placed from the lens forms a virtual image from the lens. What is the index of refraction of the lens material?