OPTI 201R 10 L17 - 17-1 6.5 F-number ! Also written as:...

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OPTI 201R Fall 2010 17-1 6.5 F-number ! Also written as: F/number, F/#, f-number, f/#, f:# (where the number sign # is replaced with the actual value, i.e. F/4, f/8, f:16, etc.) ! Also called “focal ratio”, “aperture ratio”, “relative aperture”, “f-stop”, “speed of the lens”… ! “F-numbers describe (are related to) the light gathering ability of a lens or optical system.” ! Two types of F-number calculations: ! F-numbers always have a positive value. ! F-numbers are UNITLESS!!!!!!!!! F-number (infinity) " $%&’( ) F-number (working) " $%&’( w
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OPTI 201R Fall 2010 17-2 Figure 6.12 F-number (infinity), (F/#) ) ! This definition assumes an object at - ) (parallel rays in object space). ! From the Figure: ! " # tan 2 1 /# $ $ % & lens D f F (6.39) ! From the “Abbe Sine Condition”: ! " sin 2 1 /# n D f F lens $ $ % & (6.40) ! Numerical Aperture is another measure of the ray angle: u n n NA $ ( sin sin (6.41) *+,-, . /- 01 2-, 3+, +245 -angle of the ray. NA u n F 2 1 sin 2 1 /# $ $ (6.42) F-number (infinity) " $%&’( ) ! " diameter lens length focal back diameter pupil entrance length focal back /# $ $ ( % & ent D f F (6.38)
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OPTI 201R Fall 2010 17-3 ! ! " diameter lens length focal back /# $ & F until we learn about pupils. ! The amount of light reaching the back focal plane, E image , is proportional to the area of the lens. ! " 2 2 /# 4 4 ) ) * + , , - . ) * + , - . $ $ / & % F f d A E lens image 0 so ! " 2 /# 1 & / F E image ! E image and (F/#) ) are inversely related: E image 6 27 $%&’( ) 8 E image 8 27 $%&’( ) 6 ! To change E image change the (F/#) ) : - For a given lens, the focal length is fixed . - Increase the area by making a larger diameter lens having the same focal length (smaller F-number) - Decrease the area by making a smaller diameter lens having the same focal length (larger F-number).
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This note was uploaded on 08/23/2010 for the course OPTICS 201R taught by Professor Staff during the Spring '10 term at University of Arizona- Tucson.

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OPTI 201R 10 L17 - 17-1 6.5 F-number ! Also written as:...

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