Class8

Class8 - Read Hecht, from Chapter 5: 5.7 and Chapter 6...

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Comment: matrix for reflection and the sign for the elements of the ray vector = 1 1 1 1 2 2 2 2 1 0 1 Y n R n n Y n θ = 1 0 1 D R R n n D ) ( 1 2 = Refraction: (2) = 1 1 1 1 2 2 2 1 0 2 1 Y n R n Y n = 1 0 1 D M R n D 1 2 = Reflection: (3) (n=n 1 =-n 2 ) Note : “–” sign OK = 1 0 2 1 R n M Note : det(T)=det(R)=det(M)=1
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Comment: matrix for reflection and sign convention for angles Reflection matrix: Note the sign for the ray vector: n 1 θ > 0 ( if >0); while: 2 =-n < 0 Note: Hecht textbook uses =n =n> 0 which implies a different form for the reflection matrix (see Hecht, eq. 6.39): = 1 0 2 1 ' R n M Note : det(M’)=-1 (4) Both forms of the reflection matrix (eq. 3 or eq. 4) are equally valid . Just keep in mind you have to use n=n for the ray vector if you use eq. 3 and if you use eq. 4. The advantage of eq. 3 is that it treats the reflection matrix in a similar way as the matrices for refraction and translation: det(M)=1, and 1/f=-a 12 = -2/R
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Comment: Thin Lens Equations 100 50 0 -100 -150 S i +10 cm S i +10 cm f S S i o 1 1 1 = + f=10 cm (positive lens) Image position S i Object position S o
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Eyeglasses Normal eyes : The fine focusing of human eye is performed by adjusting the crystalline lens with cilliary muscles, a muscle disc supporting the lens. By changing the focal length of lens to keep the image distance constant (on the retina, ~ 2.5 cm from the crystalline lens). For normal eyes, the far point is at infinity; and the near point, the nearest point that eye can focus, is about 25 cm. cm s i 5 . 2 = f S S i o 1 1 1 = + with (5)
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Eyeglasses Myopia (Nearsightedness): the power of the crystalline lens is too large, the parallel rays are brought to focus in front of the retina. Or the far point is closer than infinity, and all the points beyond the far point appear blurred. To correct this condition, a negative lens is introduced to diverge the ray as shown in Fig.
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Eyeglasses Hypermetropia (Farsightedness): the second focal point of relaxed eye lies behind the retina, usually due to the shortening of the axial length of the eye. As a result, its near point moves further away from the eyes, cannot see the nearby object clearly. In this case, a positive corrective lens is introduced to help imaging the nearby objects on the retina.
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Eyeglasses Dioptric power D : reciprocal of the focal length, 1D = 1m -1 Example: for thin lenses in contact, we have D = D 1 + D 2 f D 1 = glasses eye s withglasse f f f 1 1 1 + = The combined focal length for eye plus glasses: (5) Astigmatism:
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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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Class8 - Read Hecht, from Chapter 5: 5.7 and Chapter 6...

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