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Class5 - Thin Lenses in Contact In general, f.f.l. ≠...

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Unformatted text preview: Thin Lenses in Contact In general, f.f.l. ≠ b.f.l., however, if d Æ 0, that is when the lenses are brought in contact, we have: (37) 2 1 2 1 2 1 1 1 1 or . . . . . . f f f f f f f l f b l f f + = + == = If we have N thin lenses in contact: N f f f f 1 1 1 1 2 1 + ⋅ ⋅ ⋅ + + = (39) Mirrors In contrast to lenses and refracting surfaces, mirrors are reflecting optical devices. They have the advantage of working in a much broader frequency range, since they in general do not suffer any dispersion. Planar mirrors the object and its image are equidistant from the mirror surface. i S to identical is = ∴ ∆ ∆ o S VPA VAS Q Mirrors Transverse magnification for a plane mirror: Therefore, the image formed by a plane mirror is life-size, virtual and erect . 1 = − = ≡ o i o i T S S Y Y M SIGN CONVENTION for mirrors!! Plane Mirrors The image formed by a plane mirror is life-size, virtual and erect . The mirror image is inverted , i.e., left hand is imaged as right hand. Plane mirrors are frequently used to redirect a beam of light. Spherical Mirrors R R V V Convex (R>0) Concave (R<0) Spherical mirrors Spherical mirrors: ( ) r CP PCA PA θ sin sin = ∠ ( ) i SC SCA SA θ sin sin = ∠ ( ) ( ) PCA ∠ Q SCA PCA SCA o ∠ = ∠ ∴ = ∠ + sin sin 180 Law of reflection, θ i = θ r In ∆ CAP , using Law of Sines, we have: In ∆ SCA , we have: Therefore: PA CP SA SC = Spherical mirrors Spherical mirrors: PA CP SA SC = (47) PA CP SA SC = Furthermore, SC = S o-|R| and CP = |R| - S i |R| = -R by the sign convention (C on the left of vertex) Thus, SC = S o + R, CP = –(S i + R) In the paraxial region, SA ≈ S o , PA ≈ S i , and Eq. (47) becomes: R S S S R S S R S i o i i o o 2 1 1 or − = + + − = + Spherical Mirrors (48) Mirror formula R S S S R S S R S i o i i o o 2 1 1 or − = + + − = + Eq. (48) is equally applicable to concave ( R < 0) and convex ( R > 0) mirrors....
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This note was uploaded on 10/19/2009 for the course PHY 31 taught by Professor Cebe during the Fall '08 term at Tufts.

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Class5 - Thin Lenses in Contact In general, f.f.l. ≠...

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