Describe the compound microscope on the following headings: (i) Labelled ray diagram of formation of image. (ii) Magnifying power when final image is formed at least distance of distinct vision.
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Updated on : 2022-09-05
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Where O→ Objective lens, E→ Eye lens, AB→ Object, PQ→ Image. (ii) Calculation of magnification: Ratio of angle subtended by an image to the angle subtended by an object placed at least distance of distinct vision is called magnifying power of microscope. If angle subtended by an image is β and angle by an object placed at D is given by α. Therefore, magnifying power m=αβ .......(i) ∴α=DAB Where, D→ Least distance of distinct vision. As eye is close to the eye lens, we can take the angle subtended at lens for human eye also. ∴ Angle made by an image PQ β=EQPQ=EB′A′B′ or β=ucA′B′ where, uc→EB′→ Distance of image from eye lens Substituting above values in equation (i), m=DABueA′B′=ABA′B′×ueD .......(ii) Now, in similar triangle ΔA′OB′ and ΔAOB ABA′B′=OBOB′ ∴ From equation (ii), m=OBOB′×ueD or m=−uovo×−ueD (By sign convention) where, uo→OB→ Distance of object from objective lens, vo→OB′→ Distance between objective to the image A′B′ or m=uoue−VoD .......(iii) When image is formed at least distance of distinct vision: From formula: f1=v1−u1 For eye lens, fe1=−ve1−−ue1 or fe1=−ve1+−ue1 But, Ve=D ∴fe1=D1−ue1 or ue1=fe1+D1 or ueD=feD+1 Substituting this value in equation (iii), we get, m=uo−vo(1+feD) ........(iv) Formula for magnification when image is formed at D magnification.
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