Riflescope with Existing Lenses-1

Riflescope with Existing Lenses-1 - Riflescope with...

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Riflescope with Existing Lenses Section A and B (also show intermediate image planes) Section C – Summary comments The relay lens becomes the stop of the system, changing the EP, the XP and the ER: D XP = 6.25 mm D EP = 18.75 mm ER = 62.5 mm EP is 87.5 mm in front of the objective A 3x18.75 riflescope results, and you cannot meet the requirement of 3X25. Section D (also show intermediate image planes) Objective/Stop Dia = 25 mm Relay 1 Dia = 16.4 mm Eye Lens Dia = 21.3 mm XP Dia = 6.25 mm Relay 2 Dia = 22.0 mm 300 mm 75 mm 25 mm 200 mm 71.87 mm 50 mm -50 mm Objective/Stop Dia = 25 mm Relay Dia = 39.4 mm Eye Lens Dia = 19.7 mm XP Dia = 8.33 mm 116.667 mm 366.667 mm 72.22 mm 250 mm 50 mm -50 mm
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Riflescope with Existing Lenses Section A – 3X25 Riflescope with three 50 mm focal length lenses The relayed Keplerian requires three elements (objective, relay and eye lens), and the base telescope consists of just the objective and the eye lens. Since these two lenses both have the same focal length, the base MP is -1. All of the magnification (and the image erection) in the system must come from the relay stage. 3 3 11 1 50 200.0 66.667 = = =− = =+ = ′ = =− r Base Telescope r r r rr r r MP m MP z m z zzf f z z The resulting riflescope (with the marginal ray and intermediate images sketched): The XP location is found by imaging the stop first through the relay lens to an intermediate pupil, then re-imaging this pupil through the eye lens to the XP: Objective/Stop Eye Lens XP 50 -66.667 200.0 -50 116.667 250 366.667 Intermediate Pupil z p2 z p1 ER = z p2 z p1 z r z r
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Relay: 11 1 1 1 1 1 1 50 116.667 87.50 0.750 =+ = =−= = == pp pr p p p zzf f zz f z z m z Eye Lens: 22 21 2 2 2 2 2 1 50 162.5 72.22 0.444 = ′′ =− − + =− = p p p p p f f z z z z m z The XP magnification is the product of these two magnifications: 12 0.3333 XP mm m 8.33 25 = = XP XP STOP STOP EP Dm D m m D D m m This result can also be obtained directly using the riflescope MP.
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Riflescope with Existing Lenses-1 - Riflescope with...

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