91影视

An object is $60\mathrm{cm}$from a screen. What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object?

A lens placed $10\mathrm{cm}$in front of an object creates an upright image twice the height of the object. The lens is then moved along the optical axis until it creates an inverted image twice the height of the object. How far did the lens move?

A concave mirror has a $40\mathrm{cm}$radius of curvature. How far from the mirror must an object be placed to create an upright image three times the height of the object?

A $2.0\mathrm{cm}$tall object is placed in front of a mirror. A $1.0\mathrm{cm}$tall upright image is formed behind the mirror, $150\mathrm{cm}$from the object. What is the focal length of the mirror?

A spherical mirror of radius R has its center at C, as shown in FIGURE P34.78. A ray parallel to the axis reflects through F, the focal point. Prove that f = R/2 if$鈭�<<1\mathrm{rad}.$

A laser beam is incident on the left mirror in FIGURE EX$34.8$. Its initial direction is parallel to a line that bisects the mirrors. What is the angle $蠒$of the reflected laser beam?

A converging lens creates the image shown in FIGURE Q34.8. Is the object distance less than the focal length f, between f and 2 f, or greater than 2 f? Explain

Shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles ${胃}_1$and ${胃}_2$in the two media. Suppose that you did not know Snell鈥檚 law.

A. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n1 and n2

B. The time depends on x. There鈥檚 one value of x for which the light travels from A to B in the shortest possible time. We鈥檒l call it $x_{min}$. Write an expression (but don鈥檛 try to solve it!) from which $x_{min}$could be found.

C. Now, by using the geometry of the figure, derive Snell鈥檚 law from your answer to part b.

You鈥檝e proven that Snell鈥檚 law is equivalent to the statement that 鈥渓ight traveling between two points follows the path that requires the shortest time.鈥� This interesting way of thinking about refraction is called Fermat鈥檚 principle.

A fortune teller鈥檚 鈥渃rystal ball鈥� (actually just glass) is 10 cm in diameter. Her secret ring is placed 6.0 cm from the edge of the ball.

a. An image of the ring appears on the opposite side of the crystal ball. How far is the image from the center of the ball?

b. Draw a ray diagram showing the formation of the image.

c. The crystal ball is removed and a thin lens is placed where the center of the ball had been. If the image is still in the same position, what is the focal length of the lens?

Consider an object of thickness ds (parallel to the axis) in front of a lens or mirror. The image of the object has thickness ds鈥�. Define the longitudinal magnification as M = ds鈥�/ds. Prove that M = $-m^2$, where m is the lateral magnification