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4500PC07

# 4500PC07 - Close-Up Attachment Lens The general purpose...

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Unformatted text preview: Close-Up Attachment Lens The general purpose lens shown on the reverse side of this page is to be used to form an image of an object. The image is to be real (and inverted). The reproduction ratio is to be 2 to 1 (two units measured on the object become one unit measured on the image). For this situation, calculate, showing all work, the object distance .91 and the image distance 51 ’ as measured from their respective principal planes. Taking the clear aperture of the lens to be 50 mm at the object principal plane, calculate, showing all work, the solid angle subtended by the lens from a point on the object. Now a close-up attachment lens having an optical refractive power of 3.0 Diopters is added to the general purpose lens. The addition of the attachment lens correspond- ingly changes the focal length of the lens. For this new situation, calculate, showing all work, the object distance 52 and the image distance 32’ as measured from their respec- tive principal planes. Taking the clear aperture of the lens to be 50 mm at the object principal plane, calculate, showing all work, the new solid angle subtended by the lens from a point on the object. Calculate the percentage increase in the solid angle obtained by using the attach— ment lens. Express your answers accurately to four signiﬁcant ﬁgures and put them in the spaces provided below. \$1 = mm 31’ = mm solid angle = stemdians .92 == mm 32’ 2 mm solid angle with attachment lens 2 steradz'ans % increase in solid angle = % GENERAL PURPOSE IMAGING LENS Nikon 50mm (51.6mm) Nikkor-H fl2 Auto Lens Optical formula of Nikkor-H Auto 1:2 (f I 2) f = 50mm (51.6mm). Dimensions are in mm. Physical dimensions in mm of Nikkor-H Auto 1:2 (1‘ l 2) f: 50mm (51.6mm). Close-Up Attachment Lens f = 51.6mm, m = —0.5, P = 3.0Diopters, d = 50mm u1_1 s s’ — f 1 S — f(1 — a) s’ = f(1 - m) 51 = 15480771171 51 ’ = 77.40 mm Differential area on surface of sphere dA = (7* d0)(r sinﬁdqb) Differential solid angle d9 = ﬂ = sin0d6d¢ 72 Solid Angle 94 27f Q = / / sin0d6d¢ 9:0 =0 9.1 21f ¢ = —cos€ O O 27r (1 — cased) 31 tan 0d -‘= '2':- , and SO COS 0d = W _ _ A... 9 ‘ 2”<1 (s%+d2/4>1/2) Q = 0.0127912 (271') = 0.0803703teradians \Vith attachment lens 1 1 _ = ._ + P f2 f f2 = 44.6830mm 32 = 134.0492mm 32’ = 67.0246mm Q =0.0169500 (271') = 0.1065003teradians % increase in solid angle = (0.106500 -— 0.080370)/0.080370 X 100 % = 32.512 % ...
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