PHY410 Optics Exam #3

Transcription

1 PHY410 Optics Exam #3 NAME: 1

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3 Multiple Choice Section - 5 pts each 1. A continuous He-Ne laser beam (632.8 nm) is chopped, using a spinning aperture, into 500 nanosecond pulses. Compute the resultant line width λ. A nm B nm C. 150 nm D. 4.2 nm E nm 2. White light has a coherence length of about 1 µm. If a narrow band-pass filter is placed in front of a white light source, what is the coherence length of the transmitted light? The narrow band-pass filter transmits wavelengths in the range ±.1 nm. A. 4 m B. 4 cm C. 4 mm D. 4 µm E. 4 nm 3. A theoretical limiting factor governing the maximum obtainable resolution of an optical or imaging system. This definition describes which of the following terms: A. Darkfield illumination B. Chromatic aberration C. Anomalous dispersion D. Fresnel diffraction E. Diffraction limit 4. A collimated beam of mercury green light at nm is normally incident on a slit 0.15 mm wide. A lens of focal length 85 cm is placed behind the slit. A diffraction pattern is formed on a screen placed in the focal place of the lens. Determine the distance between the central maximum and the first minimum. A. 3.1 mm B. 4.2 mm C. 5.5 mm D. 7.9 mm E mm 3

4 5. What is the difference between Fresnel diffraction and Fraunhofer diffraction? A. There is no difference. Fresnel is just French for Fraunhofer B. Fresnel diffraction is only valid for geometrical optics. C. Fraunhofer diffraction is only valid in the near-field. D. Fresnel diffraction is the more general case. Fraunhofer diffraction requires a number of simplifying assumptions. E. Fraunhofer diffraction is valid for quasi-monochromatic light whereas Fresnel is valid for broadband sources. 6. Left circularly-polarized light, 1, propagates through a quarter-wave plate with the slow axis aligned vertically, / 1 0, and then through another quarter-wave plate with the slow axis 0 aligned horizontally, / 1 0. What Jones vector represents the light exiting the optical system? 0 A. 1 B. 1 C. 1 1 D. 1 0 E A Jones vector is a way to mathematically represent polarized light. If, after intense calculation, you determine the polarization of light leaving an optical system is 3, what is the polarization of the 3 light? A. Unpolarized B. Circularly polarized C. Linearly polarized D. Elliptically polarized 4

5 8. What minimum thickness should a piece of quartz have to act as a quarter-wave plate for a wavelength for nm in vacuum? The refractive indices along the slow and fast axis of the crystal are and A. 160 nm B. 1.6 µm C. 16 µm D. 160 µm E. 1.6 mm 9. An optical wave is described by the following expression: = cos!"#+% cos!"#&. This wave then passes through a quarter-wave plate where the optic axis (the fast axis) of the wave plate is parallel to the x-axis. What is the polarization of the resultant wave? A. Circularly polarized. B. Linearly polarized along the x-direction. C. Linearly polarized along the y-direction. D. Linearly polarized at an angle ±45 with the y-axis. E. Elliptically polarized. 10. For dielectric materials, the polarization, ', is related to the applied field,, by the relation ( ' ) =!! #!+ where N is the number of elementary dipoles per unit volume, e is the magnitude of the electronic charge, m is the electronic mass, + is the frictional constant,! is the frequency of the applied field, and! represents the resonance frequency for the dipoles in the medium. If!+!! and!!, then which statement is correct? A. The dipoles are oscillating in phase with the applied field. B. The dipoles are oscillating out of phase with the applied field with a phase difference of π. C. The dipoles are oscillating out of phase with the applied field with a phase difference of π/2. 5

6 Q1. (20 pts) If cadmium red line (643.8 nm) is used as a source for a Michelson interferometer, interference fringes can be discerned for a path length difference up to 30 cm. (a) What is the coherence length of the light source? (b) What is the coherence time of the light source? \ (c) What is the frequency bandwidth, ν, of the source? 6

7 Q2. (20 pts) The West Chester University observatory houses a piermounted Meade LX200 telescope with a 10-inch aperture and the focal length of 2500 mm. Visitors can view celestial objects through the telescope eyepiece or with an SBIG ST-8XME CCD camera. Advanced students can use the self-guided spectrograph for analysis of stellar atmospheres, variable stars, or for redshift measurements. For daytime observing, the Department of Physics operates a DayStar tunable Hydrogen-alpha solar filter. What is the approximate angular resolution of the telescope for the visible spectrum? Clearly show your reasoning. 7

8 Q3. (20 pts) Initially unpolarized light passes in turn through two polarizers with transmission axes at 0 and 60, respectively, relative to the horizontal. (a) What is the irradiance of the product light, expressed as a percentage of the unpolarized light irradiance? (b) A half-wave plate is inserted between the polarizers. At what angle, with respect to the horizontal, should half-wave plate be aligned so that the maximum amount of light exits the system? What is the irradiance of the product light, expressed as a percentage of the unpolarized light irradiance? 8