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HW02solutions - 24.40 Model Assume thin lenses and treat...

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24.40. Model: Assume thin lenses and treat each as a simple magnifier with 25cm/ . M f = Visualize: Equation 24.10 gives the magnification of a microscope. obj eye obj eye 25cm L M m M f f = = − Solve: (a) The more powerful lens (4 ) × with the shorter focal length should be used as the objective. (b) Solve the equation above for L (drop the negative sign). 25cm 25cm 4 2 (12)( )( ) 37.5 cm 25 cm 25 cm obj eye Mf f L = = = Assess: This is a long microscope tube.
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24.6. Model: s f W so we can use Equation 24.1: / . m f s = − Solve: 15 mm (2.0 m) 3.0 mm 10 m f h mh h s ′ = = − = − = − The height of the image on the detector is 3.0 mm. Assess: This seems reasonable given typical focal lengths and detector sizes.
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24.10. Visualize: We want the same exposure in both cases. The exposure depends on shutter . I t Δ We'll also use Equation 24.3. Solve: 2 1 exposure ( -number) I t t f = Δ ∝ Δ 2 2 1 1 ( -number) ( -number) t t f f Δ = Δ 2 2 2 2 ( -number) (4.0) 1 1 1 s s s ( -number) (5.6) 125 245 250 f t t f Δ = Δ = = Assess: An alternate approach without a lot of calculation is that since we changed the lens (opened) by one f stop that doubles the intensity so we need half the time interval to achieve the same exposure.
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24.12.
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