Chapter 11

A beam of unpolarized light is passed through two polarizers. If the polarization axis of the second polarizer is crossed at an angle of \(90^{\circ}\) with respect to the axis of the first polarizer, then the intensity of light seen by someone located to the right of the second polarizer is (A) the intensity of the original light. (B) one-half the intensity of the original light. (C) one-quarter the intensity of the original light. (D) one-eighth the intensity of the original light. (E) zero.

A beam of unpolarized light is passed through two polarizers. If the polarization axis of the second polarizer is at an angle of \(45^{\circ}\) with respect to the axis of the first polarizer, then the intensity of light seen by someone located to the right of the second polarizer is (A) the intensity of the original light. (B) one-half the intensity of the original light. (C) one-quarter the intensity of the original light. (D) one-eighth the intensity of the original light. (E) zero.

A beam of light in water \(\left(n_1=4 / 3\right)\) strikes an interface with a piece of glass \(\left(n_2=1.5\right)\). The critical angle at which total internal reflection takes place is (A) \(0^{\circ}\) (B) \(48.6^{\circ}\) (C) \(62.7^{\circ}\) (D) \(90^{\circ}\) (E) Total internal reflection cannot take place

A beam of light in glass \(\left(n_1=1.5\right)\) strikes an interface with water \(\left(n_2=4 / 3\right)\). The critical angle at which total internal reflection takes place is most nearly (A) \(0^{\circ}\) (B) \(48.6^{\circ}\) (C) \(62.7^{\circ}\) (D) \(90^{\circ}\) (E) Total internal reflection cannot take place

If in the previous problem, medium 1 is glass and medium 2 is air, which is a possible trajectory for the light beam? (A) \(\mathrm{A}\) (B) \(\mathrm{B}\) (C) \(\mathrm{C}\) (D) \(\mathrm{D}\) (E) \(\mathrm{E}\)

You are given a thin converging lens with a focal length of \(10 \mathrm{~cm}\). a) An object is placed at \(6 \mathrm{~cm}\) from the lens. Draw a ray diagram for the situation. b) Calculate the image distance. Does the calculated distance agree with the distance given by the ray diagram? Is the image real or virtual? c) The object is moved out to \(8 \mathrm{~cm}\). Draw a ray diagram for the situation. d) Calculate the image distance. Does the calculated distance agree with the distance given by the ray diagram? Is the image real or virtual. Is it larger or smaller than the image from part (a)?

You are attempting to determine the index of refraction of a block of an unknown material. You shine a light beam at various angles \(\theta_1\) from the normal to the block and measure the refraction angle \(\theta_2\), as shown. You collect the following data: $$ \begin{array}{|l|l|} \hline \theta_1(\mathrm{deg}) & \theta_2(\mathrm{deg}) \\ \hline 10 & 5.0 \\ \hline 20 & 12.5 \\ \hline 30 & 18.0 \\ \hline 40 & 24.0 \\ \hline 50 & 28.6 \\ \hline 60 & 33.0 \\ \hline 70 & 36.0 \\ \hline 80 & 40.0 \\ \hline \end{array} $$ a) Determine the index of refraction of the material by two methods. b) Which points would you say represent bad measurements? You stand at a distance \(x\) from a plane (flat) wall mirror.

A prism in the form of an equilateral triangle (below) has a refractive index \(n=1.6\). A beam of light is incident from air onto the prism at \(\theta_1=50^{\circ}\). a) What is \(\theta_2\) ? b) What is \(\theta_4\) ? c) How can the setup be changed so that total internal reflection takes place? d) A thin film of magnesium fluoride \((n=1.38)\) is painted on the left side of the prism to reduce reflection of red light \((\lambda=630 \mathrm{~nm})\) at normal incidence. What is the wavelength of the red light inside the film? e) What should be its thickness to minimize the reflection of red light? f) If the light is glancing off the prism at an angle, rather than at normal incidence, do you expect the reduction in the reflection of light to be more effective at longer or shorter wavelengths, or to remain the same?

You are given an opaque sheet of metal with a narrow slit in it, of width \(d\) (below). You are also given the following: 1) A digital timer; 2) A meter stick; 3) A metric ruler; 4) A light bulb with power cord 5) A laser pointer ( \(\lambda=630 \mathrm{~nm})\); 6) A prism; 7) A projection screen; 8) A mirror Your mission is to measure \(d\) with the proper pieces of the above equipment. a) Check off the equipment you would use. b) Draw a diagram of the experimental setup. c) Describe how you would perform the experiment. d) What would be the difference in the experiment if the metal had two narrow slits cut into it and you were asked to determine the distance between the slits?