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Light rays parallel to the optic axis are transmitted through a converging lens. They form a cone of rays on the exit side, as they come to a focus. A dimensionless quantity called the numerical aperture (NA) of the lens is defined as NA = sin a, where a is the opening angle of the cone on the exit side. (a) Find an expression for the NA in terms of the size and focal length of the lens. (b) Using your own words and diagrams, describe why interference fringes are formed at the focal point, and show that the minimum fringe spacing is 2/(2 NA). (The material of Lecture 11 will be helpful.) (c) A commercially available objective lens for a microscope is labeled "40x, 0.6", meaning 40x magnification and 0.6 NA. It is illuminated with white light having an average wavelength of 585 nm. Find the smallest object this lens can resolve, and find the image size the lens creates for this object.

Light rays parallel to the optic axis are transmitted through a converging lens. They form a cone of rays on the exit side, as they come to a focus. A dimensionless quantity called the numerical aperture (NA) of the lens is defined as NA = sin a, where a is the opening angle of the cone on the exit side. (a) Find an expression for the NA in terms of the size and focal length of the lens. (b) Using your own words and diagrams, describe why interference fringes are formed at the focal point, and show that the minimum fringe spacing is 2/(2 NA). (The material of Lecture 11 will be helpful.) (c) A commercially available objective lens for a microscope is labeled "40x, 0.6", meaning 40x magnification and 0.6 NA. It is illuminated with white light having an average wavelength of 585 nm. Find the smallest object this lens can resolve, and find the image size the lens creates for this object.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Light rays parallel to the optic axis are transmitted through a converging lens. They form a cone of rays on the exit side, as they come to a focus. A dimensionless quantity called the numerical aperture (NA) of the lens is defined as NA = sin a, where a is the opening angle of the cone on the exit side. (a) Find an expression for the NA in terms of the size and focal length of the lens. (b) Using your own words and diagrams, describe why interference fringes are formed at the focal point, and show that the minimum fringe spacing is 2/(2 NA). (The material of Lecture 11 will be helpful.) (c) A commercially available objective lens for a microscope is labeled "40x, 0.6", meaning 40x magnification and 0.6 NA. It is illuminated with white light having an average wavelength of 585 nm. Find the smallest object this lens can resolve, and find the image size the lens creates for this object.
Transcribed Image Text:Light rays parallel to the optic axis are transmitted through a converging lens. They form a cone of rays on the exit side, as they come to a focus. A dimensionless quantity called the numerical aperture (NA) of the lens is defined as NA = sin a, where a is the opening angle of the cone on the exit side. (a) Find an expression for the NA in terms of the size and focal length of the lens. (b) Using your own words and diagrams, describe why interference fringes are formed at the focal point, and show that the minimum fringe spacing is 2/(2 NA). (The material of Lecture 11 will be helpful.) (c) A commercially available objective lens for a microscope is labeled "40x, 0.6", meaning 40x magnification and 0.6 NA. It is illuminated with white light having an average wavelength of 585 nm. Find the smallest object this lens can resolve, and find the image size the lens creates for this object.
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