Estimate the linear separation of two objects on Mars that can just be resolved under ideal conditions by an observer on Earth (a) using the naked eye and (b) using the 200in.(=5.1m) Mount Palomar telescope. Use the following data: distance to Mars = 8.0×107km, diameter of pupil = 5.0mm, wavelength of light 550nm.

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At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?

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What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at θ=45°?

For the situation in Questions 9 and Fig. 1, if instead we increased the grating spacing, would (a) the half-widths of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place?

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The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See Fig.36-8b.) (a) Show that the intensity drops to one-half the maximum value when sin2α=α22. (b) Verify that α=1.39rad. (about 80°) is a solution to the transcendental equation of (a). (c) Show that the FWHM is Δθ=2sin-10.443λ/awhere a is the slit width. Calculate the FWHM of the central maximum for slit width (d) 1.00λ ,(e) 5.00λ,and (f) 10.00λ.

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With a particular grating the sodium doublet (589.00 nm and 589.59 nm) is viewed in the third order at 10° to the normal and is barely resolved. Find (a) the grating spacing and (b) the total width of the rulings.

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