PHYSICS 123: MidTerm 2

Martin J. Savage

February 1998

Department of Physics, University of Washington
Seattle, Washington 98125.

Abstract:

Dude

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A doubly-convex thin-lens has spherical faces with radius of curvature $\vert R_1\vert = 15\ {\rm cm}$ and $\vert R_2\vert = 5\ {\rm cm}$ and has a focal length of $f=2.5\ {\rm cm}$. It is placed $10\ {\rm cm}$ from a convex spherical mirror with radius of curvature $\vert R_m\vert = 4\ {\rm cm}$. An object is placed $20\ {\rm cm}$ from the lens as shown schematically in the figure on the reverse side of this page.

a) Find the refractive index of the lens.[4 pts].

b) Using the thin lens formula find the position of the image formed by the lens alone. Indicate its position and orientation on the diagram by ray-tracing. Is the image real or virtual (can it be projected onto a screen)? What is the magnification of the image? [8 pts].

c) Using the thin lens formula find the location of the image seen by looking into the mirror but not through the lens. Indicate its position and orientation on the diagram by ray-tracing. What is its magnification? [7 pts].

d) If the entire system was immersed in a transparent medium of refractive index $n_{\rm new} = 5$ what is the new focal length of the lens and the new focal length of the mirror? [6 pts].

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Figure 1: A doubly convergent thin-lens and a convex mirror.

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A laser produces an electromagnetic beam with a circular cross section of radius $10\ {\rm cm}$. [Note: You might need to use , ]

a) What is the intensity of the electromagnetic radiation in the beam? [5 pts].

b) What is the maximum value of the electric field in the beam? [8 pts].

c) An isolated cube with edges each of perfectly reflecting material sits in space at rest with respect to the laser, neglect gravity. The laser beam is directed at the cube and hits one of its faces at normal incidence. Assume the beam does not spread out as it propagates to the cube. What is the force on the cube when the beam first hits the cube. [9 pts].

d) What is the rate of energy transfer to the cube when the beam first hits the cube. [3 pts].

  

Figure 2: Laser beam.