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======Exam 2 review====== The following questions and problems are courtesy of Justin Dunlap =====Practice Questions, May 13 Lecture===== //MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. // ====Review question 1==== The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.5 cm, respectively. An object is placed 0.3 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain. What is the distance between the objective and the eyepiece? * [....] A) 11.2 cm * [....] B) 10.1 cm * [....] C) 10.4 cm * [....] D) 11.5 cm * [....] E) 9.85 cm <color green></color> ---- ====Review question 2==== A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm? * [....] A) 5.0 * [....] B) 4.0 * [....] C) 1.0 * [....] D) 3.0 * [....] E) 2.0 <color green></color> ---- ====Review question 3==== What is the power of a lens that has a focal length of $-40$ cm? * [....] A) $-4.0$ diopters * [....] B) $+4.0$ diopters * [....] C) $+2.5$ diopters * [....] D) $+2.7$ diopters * [....] E) $-2.5$ diopters <color green></color> ---- ====Review question 4==== To burn a hole in a piece of paper using light from the Sun, which mirror would work the best? * [....] A) Convex. * [....] B) Plane. * [....] C) Concave. * [....] D) All of the given answers would work equally as well. * [....] E) None of the given answers would burn a hole. <color green></color> ---- ====Review question 5==== You have a choice between two lenses of focal lengths $f_a$ and $f_b = 2 f_a$ to use as objective lens in building a compound microscope. If the magnification you obtain using lens //a// is $M_a$, what will be the magnification when using lens //b//? * [....] A) $M_b = \frac{1}{4} M_a$ * [....] B) $M_b = \frac{1}{2} M_a$ * [....] C) $M_b = 8 M_a$ * [....] D) $M_b = 4 M_a$ * [....] E) $M_b = 2 M_a$ <color green></color> ---- ====Review question 6==== Which of the following expressions is correct for the transmitted intensity of an unpolarized beam of light with an intensity $I_i$ passing through a polarizer? * [....] A) $I_t = 2 I_i$ * [....] B) $I_t = \frac{1}{2} I_i$ * [....] C) $I_t = I_i$ * [....] D) $I_t = 4 I_i$ * [....] E) $I_t = \frac{1}{4} I_i$ <color green></color> ---- ====Review question 7==== Spherical mirrors suffer from * [....] A) neither spherical nor chromatic aberration. * [....] B) chromatic aberration, but not spherical aberration. * [....] C) spherical aberration, but not chromatic aberration. * [....] D) both spherical and chromatic aberration. <color green></color> ---- ====Review question 8==== A nearsighted person has a far point that is 4.2 m from his eyes. What focal length lenses must he use in his contact lenses to allow him to focus on distant objects? * [....] A) $-5.2$ m * [....] B) $4.8$ m * [....] C) $4.2$ m * [....] D) $-4.2$ m * [....] E) $5.2$ m <color green></color> ---- ====Review question 9==== Jill is farsighted and cannot see objects clearly that are closer to the eye than 80.0 cm. What is the focal length of the contact lenses that will enable her to see objects at a distance of 25.0 cm from her eyes? * [....] A) $+32.5$ cm * [....] B) $-36.4$ cm * [....] C) $-21.2$ cm * [....] D) $+36.4$ cm * [....] E) $+21.2$ cm <color green></color> ---- ====Review question 10==== An object is placed in front of a convex mirror at a distance larger than twice the focal length of the mirror. The image will appear * [....] A) upright and enlarged. * [....] B) upright and reduced. * [....] C) inverted and enlarged. * [....] D) inverted and reduced. * [....] E) in front of the mirror. <color green></color> ---- ====Review question 11==== Which one of the following is the correct number for the magnification of a plane mirror? * [....] A) 2.0 * [....] B) 1.5 * [....] C) 1.0 * [....] D) 0.25 * [....] E) 0.5 <color green></color> ---- ====Review question 12==== A vertically polarized beam of light of intensity $100\frac{\text W}{\,{\text m}^2}$ passes through a polarizer with its transmission axis at 40.0$^\circ$ to the vertical. What is the transmitted intensity of this beam of light? * [....] A) $58.7\frac{\text W}{\,{\text m}^2}$ * [....] B) $0\frac{\text W}{\,{\text m}^2}$ * [....] C) $100\frac{\text W}{\,{\text m}^2}$ * [....] D) $44.4\frac{\text W}{\,{\text m}^2}$ * [....] E) $25.0\frac{\text W}{\,{\text m}^2}$ <color green></color> ---- ====Review question 13==== The length of a telescope is 2.00 m and the focal length of the objective is 2.0 cm. What is the focal length of the eyepiece? * [....] A) 200 cm * [....] B) 101 cm * [....] C) 198 cm * [....] D) 202 cm * [....] E) 2.0 cm <color green></color> ---- ====Review question 14==== John's face is 20 cm in front of a concave shaving mirror of focal length 30 cm. How large an image does he observe? * [....] A) of the same size as his face * [....] B) twice as large as his face * [....] C) half as large as his face * [....] D) four times as large as his face * [....] E) three times as large as his face <color green></color> ---- ====Review question 15==== A simple refracting telescope provides large magnification by employing * [....] A) a long focal length objective and a long focal length eyepiece. * [....] B) a short focal length objective and a long focal length eyepiece. * [....] C) a short focal length objective and a short focal length eyepiece. * [....] D) a long focal length objective and a short focal length eyepiece. <color green></color> ---- =====Practice Problems, May 13 Lecture===== //Solve three of the four problems (cross out the one you do not want graded). Show all of your work to receive full credit, most importantly show all the formulas you used to find the final answers. No credit will be awarded if an answer is given without work shown.// ---- ====Review problem 1==== {{ :figs:ex2rev1.png?nolink |}} The lens system above has focal lengths $f_1 = 45.0$ cm, $f_2 = -50.0$ cm, object height $h_o = 40.0$ cm, the distance of the object from the first lens $d_o = 70.0$ cm, and the distance between the two lenses equal to $L=200$ cm: * a) Using at least two light rays, on the drawing above sketch the location and size of the image after passing through the first lens as well as the location and size of the final image. (You may change which two rays you use for each lens.) (4 pts) * <color green>...</color> * <color green>...</color> * b) How far away is the final image from the object? (6 pts) * <color green>...</color> * <color green>...</color> * c) What is the total magnification of the two lens system? (3 pts) * <color green>...</color> * <color green>...</color> * d) What is the height of the final image? (2 pts) * <color green>...</color> * <color green>...</color> ====Review problem 2==== A meter stick lies along the principal axis of a convex mirror with a focal length of 30.0 cm. Two 10.0 cm toy figures are placed upright on near and far end of the meter stick. The closer of the two figures is 50.0 cm away from the mirror. {{ :figs:ex2rev2.png?nolink| }} * a) How far away from the mirror is the image of the figure that is closest to the mirror? (4 pts) * <color green>...</color> * <color green>...</color> * b) How far away from the mirror is the image of the figure that is furthest from the mirror? (4 pts) * <color green>...</color> * <color green>...</color> * c) What is the length of the image of the meter stick? (in other words, what is the distance between the two images of the figures?) (1 pts) * <color green>...</color> * d) How tall is the closer of the two figures to the mirror in the image? (2 pts) Is it upright or inverted? (1 pt) * <color green>...</color> * <color green>...</color> * e) How tall is the farther of the two figures from the mirror in the image? (2 pts) Is it upright or inverted? (1 pt) * <color green>...</color> ---- ====Review problem 3==== Match the definitions and descriptions with the best term or phrase given below (1.5 pts each): | Resonance \\ Underdamping \\ Critical damping \\ Overdamping \\ Period \\ Frequency \\ Angular frequency \\ Wavelength \\ Simple pendulum \\ Physical pendulum \\ Transverse wave \\ Longitudinal wave \\ Linear mass density | Wave function \\ Reflections \\ Ultrasound \\ Intensity \\ Decibel \\ Doppler effect \\ Superposition \\ Constructive interference \\ Destructive interference \\ Standing wave \\ Fundamental frequency \\ 2<sup>nd</sup> Harmonic frequency \\ 3<sup>rd</sup> Harmonic frequency | Beat frequency \\ In-phase sources \\ Opposite phase sources \\ Direction of propagation of light \\ Speed of light in a vacuum \\ Microwaves \\ Radio waves \\ Infrared \\ Visible \\ Ultraviolet \\ x-rays \\ Gamma rays | - Two sources that emit crests at the same time and emit troughs at the same time. * <color green>In-phase sources</color> - Ninety degrees to both the electric field and the magnetic field in a moving electromagnetic wave. * <color green>Direction of propagation of light</color> - Energy per unit time per unit area. * <color green>Intensity</color> - A measure of sound intensity. Increasing by about three of these units will indicate a doubling of the intensity of the sound. * <color green>Decibel</color> - When two waves combine to create a wave with an amplitude less than either of the two original waves. * <color green>Destructive interference</color> - A part of the electromagnetic spectrum with frequencies just greater than those visible by humans. * <color green>Ultraviolet</color> - A point mass on the end of a mass-less string that is allowed to swing back and forth. * <color green>Simple pendulum</color> - A wave where the direction of the molecules is perpendicular to the direction of the wave. * <color green>Transverse wave</color> - The lowest frequency that can be created on a string or in a tube. * <color green>Fundamental frequency</color> - The length of time between two wave crests. * <color green>Period</color> ---- {{ :figs:ex1rev3.jpg?292|}} ====Review problem 4==== The air pressure variations in a sound wave cause the eardrum (tympanic membrane) to vibrate. - For a given vibration amplitude, are the maximum velocity and acceleration of the eardrum greatest for high frequency sounds or low frequency sounds? (1 pts) * <color green>$v_\text{max}$ $=x_\text{max}\omega$</color> * <color green>$a_\text{max}$ $=x_\text{max}\omega^2$</color> * <color green>the greatest values are for the high-frequency sound</color> - Find the maximum velocity and the maximum acceleration of the eardrum for vibrations of amplitude $1.0\times 10^{-8}\,$m at a frequency of 20.0 kHz. (5 pts) * <color green>$v_\text{max}$ $=x_\text{max}\omega$ $=x_\text{max}(2\pi f)$ $=1.0\times 10^{-8}\,$m$\,\cdot\,6.283\cdot 20\times 10^3\,$Hz $=1.26\times 10^{-3}\frac{\text m}{\text s}$ </color> * <color green>$a_\text{max}$ $=x_\text{max}\omega^2$ $=x_\text{max}(2\pi f)^2$ $=1.0\times 10^{-8}\,$m$\,\cdot\,(6.283\cdot 20\times 10^3\,$Hz$)^2=158\,\frac{\text m}{\,{\text s}^2}$ </color> - What is the period of a complete oscillation of the ear drum at this frequency? (2 pts) * <color green>$T=\frac{1}{f}$ $=\frac{1}{20\times 10^3\,{\text{Hz}}}$ $=5.0\times 10^{-5}\,$s</color> - Using a crude model of the eardrum as a mass (3.0 mg) on a spring, what would be the spring constant of the eardrum, assuming the resonance frequency of 20.0 kHz? (3 pts) * <color green>$T=2\pi\sqrt{\frac{m}{k}}$</color> * <color green>$\left(\frac{T}{2\pi}\right)^2=\frac{m}{k}$</color> * <color green>$k=\frac{4\pi^2m}{T^2}$ $=\frac{4\,\cdot\,3.14159^2\,\cdot\,3.0\times 10^{-6}\,{\text{kg}}}{\big(5.0\times 10^{-5}\,{\text s}\big)^2}$ $=4.74\times 10^4\frac{\text N}{\text m}$</color> - The ear canal (external auditory canal) can be modeled as a tube with one closed end. If the length of the ear canal is 25 mm long and the speed of sound in air is 340 m/s, what is the fundamental (1<sup>st</sup> harmonic) of the ear canal? (4 pts) * <color green>$f_1=\frac{v}{4L}$ $=\frac{340\,\frac{\text m}{\text s}}{4\,\cdot\,25\times 10^{-3}\,{\text m}}$ $=3400\,$Hz</color>

exam_2_review.1399687900.txt.gz · Last modified: 2014/05/10 02:11 by wikimanager