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Related Concept Videos

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Boundary Layer Characteristics

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Interference and Diffraction02:18

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Related Experiment Video

Updated: Jun 15, 2026

The 4 Mountains Test: A Short Test of Spatial Memory with High Sensitivity for the Diagnosis of Pre-dementia Alzheimer's Disease
06:23

The 4 Mountains Test: A Short Test of Spatial Memory with High Sensitivity for the Diagnosis of Pre-dementia Alzheimer's Disease

Published on: October 13, 2016

Mountain shadow phenomena.

W Livingston, D Lynch

    Applied Optics
    |March 9, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Mountain peaks cast triangular shadows when the sun is low, regardless of their shape. A new theory explains these anomalous shadows, showing the shadow angle depends solely on the mountain's breadth-to-height ratio.

    Related Experiment Videos

    Last Updated: Jun 15, 2026

    The 4 Mountains Test: A Short Test of Spatial Memory with High Sensitivity for the Diagnosis of Pre-dementia Alzheimer's Disease
    06:23

    The 4 Mountains Test: A Short Test of Spatial Memory with High Sensitivity for the Diagnosis of Pre-dementia Alzheimer's Disease

    Published on: October 13, 2016

    Area of Science:

    • Geophysics
    • Optical physics
    • Mountain observation

    Background:

    • Mountain peaks often appear to cast triangular shadows when observed from their summits, particularly during sunrise or sunset.
    • The precise geometric explanation for this phenomenon, irrespective of the mountain's specific profile (e.g., flat-topped or pointed), has been a subject of interest.

    Purpose of the Study:

    • To develop a theoretical framework explaining the formation of triangular shadows cast by mountain peaks.
    • To determine the key factors influencing the apex angle of these anomalous mountain shadows.

    Main Methods:

    • Development of a geometric optics theory.
    • Mathematical analysis of shadow formation based on mountain geometry.

    Main Results:

    • A theory is presented that accounts for the triangular shadows observed from mountain summits.
    • The study demonstrates that the shadow apex angle is exclusively determined by the ratio of the mountain's breadth to its height.

    Conclusions:

    • The observed triangular shadows from mountain peaks are a predictable geometric outcome.
    • The breadth-to-height ratio is the sole determinant of the apex angle in these mountain shadows, offering a simplified model for understanding this optical phenomenon.