Exam 27: Magnetic Field and Magnetic Forces

Refraction at a curved surface: The left-hand end of a glass rod is ground to a spherical surface. The glass has index of refraction 1.50. A small object 4.00 mm tall is placed on the axis of the rod, 37.0 cm to the left of the vertex of the spherical surface. The image is formed in the rod, 50.0 cm to the right of the vertex. (a) What is the magnitude of the radius of curvature of the spherical surface at the end of the rod? (b) What is the height of the image?

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

Compound microscope: The objective and the eyepiece of a microscope have focal lengths of 4.00 mm and 25.0 mm, respectively. The objective produces a real image 30 times the size of the object. The final image is viewed at infinity, and the near point of the microscope user is at 25.0 cm. What is the distance between the object and the focal point of the objective?

Thin lenses: In the figure, the image is viewed on a screen and is 13.5 mm tall. What is the focal length of the lens?

Lens-maker's formula: A convex-concave thin lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm. If the glass used has index of refraction 1.500, what is the focal length of this lens?

Thin lenses: A 4.0-cm tall object is placed 50.0 cm from a diverging lens having a focal length of magnitude 25.0 cm. What are the nature and location of the image? The image is

Refraction at a curved surface: A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed. How deep does the stream appear to the fisherman? The index of refraction of the water is 1.33.

Total internal reflection: 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 reaches the brine-oil interface at the critical angle. What is the distance of this point from the axis?

Lens-maker's formula: A lens is made with a focal length of -40 cm using a material with index of refraction 1.50. A second lens is made with the SAME GEOMETRY as the first lens, but using a material having refractive index of 2.00. What is the focal length of the second lens?

Thin lenses: An optical system comprises in turn, from left to right: an observer, a lens of focal length +30 cm, an erect object 20 mm high, and a convex mirror of radius 80 cm. The object is between the lens and the mirror, 20 cm from the lens and 50 cm from the mirror. The observer views the image that is formed first by reflection and then by refraction. What is the position of the final image, measured from the mirror?

Refraction at a curved surface: A swimming pool is filled to a depth of 2.0 m. How deep does the pool appear to be from above the water, which has an index of refraction of 1.33?

Eyes: A myopic (nearsighted) dancer wears eyeglasses that allow him to have clear distant vision. The power of the lenses of his eyeglasses is - 3.00 diopters. Without eyeglasses, what is the far point of the dancer?

Eyes: The near point of a person's uncorrected eyes is 125.0 cm and the far point is at infinity. What is the focal length of a contact lens that will move the near point to 25.0 cm from this person's eyes?

Snell's law: Light strikes a 5.0-cm thick sheet of glass at an angle of incidence in air of 50°. The sheet has parallel faces and the glass has an index of refraction 1.50. (a) What is the angle of refraction in the glass? (b) After traveling through the glass the light re-emerges into the air. What is the final angle of refraction in air? (c) As it leaves the glass, by what distance is the path of the ray is displaced from what it was before entering the glass?

Thin lenses: An object is placed 10 cm from a convex lens of focal length 20 cm. What is the lateral magnification of the object?

Eyes: A person's eye lens is 2.7 cm away from the retina. This lens has a near point of 25 cm and a far point at infinity. (a) What must the focal length of this lens be in order for an object placed at the near point of the eye to focus on the retina? (b) What must the focal length of this lens be in order for an object placed at the far point of the eye to focus on the retina?

Spherical mirrors: A convex spherical mirror with a focal length of magnitude 25 cm has a 4.0-cm tall flower placed 100 cm in front of it. What is the height of the image of the flower?

Thin lenses: An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. If the height of the object is 6.0 cm, what is the height of the final image?

Thin lenses: A 4.0-cm tall object is placed 60 cm away from a converging lens of focal length 30 cm. What are the nature and location of the image? The image is

Spherical mirrors: An object is 12 cm in front of a concave spherical mirror, and the image is 3.0 cm in front of the mirror. What is the focal length of the mirror?