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19.4: Image Formation

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  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    When a convex lens is placed between the mask and the screen, the optical bench can form magnified images of the mask onto the screen. Use of a mirror can simply extend the effective screen distance. Note: caution should be taken when using a mirror to reflect laser light.

    Optical bench set up for image formation

    The distance between the object and lens (u), the distance between the image and lens (v) and the focal length of the lens (f) are related by the equation


    Diagram of image formation with a convex lens

    Distances involved

    A lens will focus light from infinity to the 'focal point', at a distance from the lens known as the focal length, f. Located at the focal point, is the back focal plane of the lens where the diffraction pattern is visible (by using a screen). The diffraction pattern acts as a source of light that propagates to the screen where the image is formed. This theory was first described by Ernst Abbe in 1872.

    Diagram of mask, lens, back focal plane and screen showing image formation

    The diffraction pattern of a mask without a centre of symmetry will still be symmetrical. This can be seen in the mathematics of calculating the pattern. The non-centrosymmetric nature of the mask will however cause non-centrosymmetric variations in the phase.

    This page titled 19.4: Image Formation is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS).

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