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GEOMETRICAL OPTICS, :checkered_flag: The minimum length of the mirror…
GEOMETRICAL OPTICS
Plane Surfaces
Reflection 
Image Formation
:checkered_flag: Reflection of smooth surfaces such as mirrors or a calm body of water is known as specular reflection.
:checkered_flag: Reflection of rough surfaces such as clothing, paper and the asphalt roadway leis known as diffuse reflection
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Spherical surfaces
Reflection
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Thin lenses
Lensmaker's Equation
At the first refracting surface of radius R1,
Equation 1 At the second refracting surface of radius R2,
Equation 2 Assumption: lens faces the same medium of refractive index n1 on both sides. The second object distance is given by,
Equation 3 where t is the thickness of the lens. This relationship produces the correct sign of s2.Neglecting t for the thin lens approximation,
Equation 4 Combine, The focal length of the thin lens is defined as the image distance for an object at infinity, or the object distance for an image at infinity, giving, This equation is calles as lensmaker's equation because it predicts the focal length of a lens fabricated with a given refractive index n1. In most cases, the ambient medium is air and n1 = 1. The thin lens equation, in terms of the focal length, is then
Wavefront analysis of thin lenses (a) Action of convergence lens on plane wavefronts of light
(b) Action of divergence lens on plane wavefronts of light Figure above indicates that a lens thicker in the middle causes convergence, while one thinner in the middle causes divergence of the incident parallel rays.Plane waves with flat wavefronts arriving at a thin lens are curved to stay isochronous.
Graphical ray tracing of the thin lens Ray diagrams for image formation by (a) a convex lens and (b) a concave lens. Magnification of the thin lenses, With proper sign convention. In case, (a) s>0 , s'>0 , and m<0 because the image is inverted (b) s>0 , s'<0 , and m>0. In either case then, :pencil2: m > 0 for images with the same orientation as objects.:pencil2: m < 0 for inverted images.
Ray tracing in combine systems (a) Formation of a virtual image by a two-element train of a convex lens (1) and concave lens (2).
(b) Formation of a real image RI2 by a train of two convex lenses. The intermediate image RI1 serves as a virtual object VO2 for for the second lens.
:checkered_flag: The minimum length of the mirror required to form full size image of the object is half the size of the object.
:checkered_flag: Has the same distance as object to the mirror and laterally reversed.
:checkered_flag: Image is virtual and has the same size as the object.
Sign Convention for Magnification
:zap: The distance from the object to the lens/mirror is object distance [s]. Positive if it is on the same side of the optical element as the incoming light.
:zap: The distance from the image to the lens/mirror is called image distance [s']. Positive if it is on the same side as the outgoing light.
:eyeglasses: When paraxial light rays from a distant object strike a concave mirror, a real image is produced at the focal point in front of the mirror.
:eyeglasses: When paraxial light rays from distant object to the principal axis strike a convex mirror, the rays appear to originate from an focal point behind the mirror.
:eyeglasses: The image is virtual
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