Exam 23: Ray Optics

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?

An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)

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?

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?

An optic fiber is made of clear plastic with index of refraction of 1.50, surrounded by air. For what angles of incidence θ will light remain within the plastic fiber?

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)

A compound lens is made by joining the plane surfaces of two thin plano-convex lenses of different glasses. The radius of curvature of each convex surface is 80 cm. The indices of refraction of the two glasses are 1.50 and 1.60. What is the focal length of the compound lens?

A thin double convex lens is to focus the image of an object onto a screen so that the image is life-sized. The lens surfaces have equal radii of curvature of 112 cm, and the refractive index of the lens material is 1.500. (a) How far from the lens should the screen be placed? (b) How far is the screen from the object?

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?

A concave spherical mirror with a radius of 20 cm creates a real image 30 cm from the mirror. How far is the object from the mirror?

An object 1.80 cm tall is placed 100 cm in front of a diverging lens having a focal length of magnitude 25 cm. A converging lens with a focal length of magnitude 33.33 cm is placed 30 cm past the first lens. What is the lateral magnification of this system of lenses?

An object 4.0 cm in height is placed 8.0 cm in front of a concave spherical mirror with a focal length of 10.0 cm. What is the position of its image in relation to the mirror, and what are the characteristics of the image?

A beam of light of two different wavelengths enters a pane of glass 3.00 mm thick at an angle of incidence of 56°. The indices of refraction for the two different colors are 1.514 and 1.528. Because of dispersion, the colored beams, although parallel, are separated by a small distance. How far apart are they?

The critical angle in air for a particular type of glass is 39.0°. What is the speed of light in this class glass? (c = 3.00 × 10⁸ m/s)

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

In the figure, the thin lens forms a real image of the object 94.0 cm from the object. What is the focal length of the lens?

A goldfish bowl is spherical, 8.0 cm in radius. A goldfish is swimming 3.0 cm from the wall of the bowl. Where does the fish appear to be to an observer outside? The index of refraction of water is 1.33. Neglect the effect of the glass wall of the bowl.

When an object 1.15 cm tall is placed 12 cm from a lens, the lens produces an upright image of the object that is 5.75 cm tall. What is the focal length of the lens?

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?

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?