This preview shows pages 1–10. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 lifesize, 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 lifesize, 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 oR 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....
View
Full
Document
This note was uploaded on 10/19/2009 for the course PHY 31 taught by Professor Cebe during the Fall '08 term at Tufts.
 Fall '08
 CEBE

Click to edit the document details