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Physics: Spherical Mirror Curvature and Electromagnetic Spectrum Questions
Physics
Grade 10 of Junior High School (German Education System)
Question Content
10) Die Teilaufgaben sind getrennt lösbar\n a) Beurteilen Sie die Brennweite und den Mittelpunkt eines Hohlspiegels und eines Weitspiegels, wenn man jeweils ihre Krümmungen vergrößern würde. (2P)\n b) Zeichnen Sie geordnet die Regenbogenfarben und die UV und IR Strahlen. Markieren Sie, welche der Farben die höchste und welche die niedrigste Energie besitzt (4P)
Correct Answer
a) For concave mirror: Increasing curvature shortens focal length, focal point moves closer to mirror; center of curvature moves closer to mirror. For convex mirror: Increasing curvature shortens focal length, focal point moves closer to mirror; center of curvature moves closer to mirror (on the back side).\n b) Ordered spectrum (left to right, increasing energy): IR, Red, Orange, Yellow, Green, Blue, Violet, UV. Highest energy: UV; Lowest energy: IR
Detailed Solution Steps
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Step 1 (Part a): Recall mirror formulas: For spherical mirrors, focal length f = R/2, where R is radius of curvature. Curvature is inversely related to radius of curvature (larger curvature = smaller R).
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Step 2 (Part a): For concave mirror: If curvature increases, R decreases, so f = R/2 decreases. Focal point and center of curvature both move closer to the mirror surface.
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Step 3 (Part a): For convex mirror: If curvature increases, R (negative value in sign convention) becomes more negative, so f = R/2 becomes more negative (shorter magnitude, closer to mirror). Center of curvature and focal point move closer to the back of the mirror.
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Step 4 (Part b): Recall electromagnetic spectrum order: Infrared (IR) has longer wavelength than visible light; visible light order is Red < Orange < Yellow < Green < Blue < Violet in energy; Ultraviolet (UV) has shorter wavelength than visible light.
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Step 5 (Part b): Energy is inversely proportional to wavelength (E = hc/λ), so order from lowest to highest energy is IR, Red, Orange, Yellow, Green, Blue, Violet, UV. Mark UV as highest energy, IR as lowest energy.
Knowledge Points Involved
1
Spherical Mirror Focal Length and Curvature
For all spherical mirrors, the focal length f is half the radius of curvature R (f = R/2). Curvature is a measure of how sharply the mirror curves; increasing curvature means decreasing radius of curvature. For concave mirrors, focal point and center of curvature are in front of the mirror; for convex mirrors, they are behind the mirror. This formula applies to thin spherical mirrors in geometric optics.
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Electromagnetic Spectrum Order and Energy
The electromagnetic spectrum includes infrared (IR), visible light, and ultraviolet (UV) radiation. Visible light ranges from red (longest wavelength) to violet (shortest wavelength). Energy of electromagnetic radiation is given by E = hc/λ, where h is Planck's constant, c is speed of light, and λ is wavelength. Shorter wavelength means higher energy, so UV has higher energy than visible light, and IR has lower energy than visible light.
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Visible Light Spectrum
The visible light spectrum is the portion of the electromagnetic spectrum visible to the human eye, ordered from lowest to highest energy: Red, Orange, Yellow, Green, Blue, Violet. This order is seen in rainbows, formed by dispersion of white light through water droplets.
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