Download Diffraction Grating - Optics and Modern Physics - Past Paper and more Exams Physics in PDF only on Docsity! 1003. A source containing a mixture of two isotopes of the same ele- ment emits light at two wavelengths whose average value is 495 nm and whose separation is 0.0962 nm. Find the minimum num- ber of lines needed in a diffraction grating that can resolve these lines in second order. 16. A ray of light goes from air into a flat block of glass (index of refraction = 1.5) at an angle of 36◦ with the normal to the in- terface. After passing through the glass, at what angle to the normal will the ray emerge into air? a) 67◦ b) 62◦ c) The ray won’t emerge into air, be- cause it will be totally internally re- flected in the glass. d) 36◦ e) 23◦ 36o θ Air Glass n=1.5 17. When the rectangular metal tank in the figure is filled to the top with an unknown liquid, an observer (in air) with eyes level with the top of the tank can just see the corner, E. What is the index of refraction of the liquid? a) 1.64 b) 1.5 c) 1.29 d) 1.26 e) .77 Observer 1.10 m 85 cm E 18. Which of the following quantities remains unchanged when light passes from a vacuum into a slab of glass with a 45◦ angle of incidence a) its polarization b) its direction of travel c) its frequency d) its wavelength e) its speed 19. A concave mirror forms a real image which is twice the size of the object. If the object is 20 cm from the mirror, the radius of curvature of the mirror must be about: a) 27 cm b) 40 cm c) 20 cm d) 80 cm e) 13 cm 20. A concave mirror has focal length f > 0. A real object is placed a distance 2f from the mirror. Then the image is a) Real; inverted; same size as object b) Virtual; upright; bigger c) Real; inverted; bigger d) Virtual; upright; smaller e) Real; inverted; smaller 21. An object is placed 12 cm from a lens. The image is upright and one-third as big as the object. What is the focal length of the lens? a) +6 cm b) +9 cm c) +18 cm d) +3 cm e) −6 cm 1 22. In a double slit interference experiment, the angular spacing be- tween the second and third maxima on the left is observed to be 2◦. What is the ratio of wavelength to slit spacing, λ/d? a) 0.91 b) .011 c) .035 d) 2 e) .5 23. Monochromatic light is normally incident on a grating which is 1 cm wide and has 10,000 slits. The first order maximum is deviated at a 30◦ angle. What is the wavelength of the incident light? a) 600 nm b) 500 nm c) 400 nm d) 1,000 nm e) 300 nm 24. A beam of X-rays is incident on a crystal whose planes of atoms have a spacing of 0.314 nm. A second-order maximum is observed for diffracted x-rays making an angle of 24.1◦ with the plane of atoms. What is the wavelength of these X-rays? a) About 0.52 nm b) About 0.39 nm c) About 0.13 nm d) About 1.04 nm e) About 0.26 nm 25. An unpolarized beam of light is incident on three parallel polariz- ing sheets that are lined up so that the tranmission axis of each is rotated by 30◦ with respect to the preceding sheet. What fraction of the incident intensity is transmitted? a) 1/8 b) 9/32 c) 3/8 d) 27/64 e) 1/3 26. A few years ago, the Metropolitan Museum of Art in New York City featured a special exhibition of the work of the Impressionist painter Georges Seurat, who used a technique called ”pointillism”, in which his paintings are composed of small, closely-spaced dots of pure color, each about 2 mm in diameter. From what min- imum distance should the paintings be viewed to maintain the illusion of the colors blending together smoothly in the eye of the viewer? Take the pupil diameter of the eye to be 3 mm, and use a wavelength of 400 nm. (This choice is near the minimum of the visible spectrum, so as to assure that the illusion is present for all wavelengths). a) About 1 meter b) About 15 m c) About 30 meters d) About 12 meters e) About 500 cm 27. A camera lens is coated with a thin film to eliminate reflection of light whose wavelength is λA in air and λF in the film. The index of refraction of the film is less than that of the lens. What must the thickness of the coating be? a) λF/4 b) λF c) λA/2 d) λF/2 e) λA/4 2
