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Optical Instruments - Simple and Compound Microscope

An object of height \( 5 \, \text{cm} \) is placed \( 30 \, \text{cm} \) from a concave mirror of focal length \( 15 \,

**Compound microscope** M = m_o × M_e, objective magnification m_o = v_o/u_o ≈ L/f_o, L tube length, eyepiece M_e = 1+D/f_e (image at D) or D/f_e (infinity). Objective forms real inverted magnified image at focal plane of eyepiece, eyepiece acts as simple microscope magnifying it. Focal length: f = -15 cm , u = -30 cm . Mirror equation: (1/v) + (1/-30) = (1/-15) ⇒ (1/v) = (1/-15) + (1/30) = (-2 + 1/30) = (-1/30) . v = -30 cm . Magnification: m = -(v/u) = -(-30/-30) = -1 . Image height: h' = m × h = -1 × 5 = -5 cm

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Optical Instruments - Simple and Compound Microscope

An object of height \( 4 \, \text{cm} \) is placed \( 16 \, \text{cm} \) from a concave mirror of focal length \( 8 \, \

**Microscope principle** objective of short focal length forms real image between F_e and 2F_e of eyepiece, eyepiece magnifies to virtual image at D, total magnification product, for f_o=2 cm, f_e=5 cm, L=20 cm, m_o≈10, M_e≈6, M≈60, illustrating high magnification from two stages. Focal length: f = -8 cm , u = -16 cm . Mirror equation: (1/v) + (1/-16) = (1/-8) ⇒ (1/v) = (1/-8) + (1/16) = (-2 + 1/16) = (-1/16) . v = -16 cm . Magnification: m = -(v/u) = -(-16/-16) = -1 . Image height: h' = m × h = -1 × 4 = -4 cm (inverted). Magnitude =

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Optical Instruments - Simple and Compound Microscope

An object of height \( 3 \, \text{cm} \) is placed \( 15 \, \text{cm} \) from a concave mirror of focal length \( 10 \,

**Simple microscope** magnification M = 1 + D/f when image at D=25 cm near point, M = D/f when image at infinity (relaxed eye), f focal length (cm), D least distance of distinct vision 25 cm. For f=4 cm, image at 25 cm, M=1+25/4=7.25, angular magnification ratio of angle subtended by image to that by object at D. Focal length: f = -10 cm , u = -15 cm . Mirror equation: (1/v) + (1/-15) = (1/-10) ⇒ (1/v) = (1/-10) + (1/15) = (-3 + 2/30) = (-1/30) . v = -30 cm . Magnification: m = -(v/u) = -(-30/-15) = -2 . Image

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Optical Instruments - Simple and Compound Microscope

A concave mirror has a radius of curvature of \( 40 \, \text{cm} \). An object of height \( 2 \, \text{cm} \) is placed

**Compound microscope** M = m_o × M_e, objective magnification m_o = v_o/u_o ≈ L/f_o, L tube length, eyepiece M_e = 1+D/f_e (image at D) or D/f_e (infinity). Objective forms real inverted magnified image at focal plane of eyepiece, eyepiece acts as simple microscope magnifying it. Focal length: f = (R/2) = (-40/2) = -20 cm (negative for concave mirror). Object distance: u = -30 cm . Using mirror equation: (1/v) + (1/u) = (1/f) . (1/v) + (1/-30) = (1/-20) ⇒ (1/v) = (1/-20) + (1/30) = (-3 + 2/60) = (-1/60) . v = -60 cm (real image). Magnification: m = -(v/u) = -(-60/-30)

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Optical Instruments - Simple and Compound Microscope

An object of height \( 3 \, \text{cm} \) is placed \( 20 \, \text{cm} \) from a concave mirror of focal length \( 15 \,

**Microscope principle** objective of short focal length forms real image between F_e and 2F_e of eyepiece, eyepiece magnifies to virtual image at D, total magnification product, for f_o=2 cm, f_e=5 cm, L=20 cm, m_o≈10, M_e≈6, M≈60, illustrating high magnification from two stages. f = -15 cm , u = -20 cm . (1/v) + (1/-20) = (1/-15) ⇒ (1/v) = (1/-15) + (1/20) = (-4 + 3/60) = (-1/60) . v = -60 cm . Magnification: m = -(v/u) = -(-60/-20) = -3 . Image height: h' = m × h = -3 × 3 = -9 cm (inverted). Magnitude = 9 cm . Substituting

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