#eyepiece

Telescope, Human Eye and Defects of Vision

A telescope has an objective of focal length \( 150 \, \text{cm} \) and an eyepiece of focal length \( 5 \, \text{cm} \)

**Astronomical telescope** in normal adjustment M = -f_o/f_e, f_o objective focal length (m), f_e eyepiece focal length, length L = f_o+f_e, final image at infinity, angular magnification ratio of angles subtended by image and object. For f_o=100 cm, f_e=5 cm, M=-20, inverted, used for celestial observation. Magnifying power: m = (f_o/f_e) . f_o = 150 cm , f_e = 5 cm . m = (150/5) = 30 . Substituting values gives 30, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.

Ref: NCERT > Physics Book > Ray Optics > Telescope, Human Eye and Defects of Vision

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Combination of Lenses and Lens Systems

A compound microscope has an objective of focal length \( 2 \, \text{cm} \) and tube length \( 20 \, \text{cm} \). If th

**Two lenses in contact** behave as single lens with power sum, magnification product m = m₁×m₂. For f₁=20 cm (P₁=5 D), f₂=-20 cm (P₂=-5 D) in contact, P=0, F infinite, afocal system, beam emerges parallel, principle of corrective lenses for myopia/hypermetropia. Objective magnification: m_o = (L/f_o) . L = 20 cm , f_o = 2 cm ⇒ m_o = (20/2) = 10 . Eyepiece magnification: m_e = 5 (given). Total magnification: m = m_o × m_e = 10 × 5 = 50 . Substituting values gives 50, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f

Ref: NCERT > Physics Book > Ray Optics > Combination of Lenses and Lens Systems

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Combination of Lenses and Lens Systems

A compound microscope has an objective of focal length \( 1.25 \, \text{cm} \) and eyepiece of focal length \( 5 \, \tex

**Two lenses in contact** behave as single lens with power sum, magnification product m = m₁×m₂. For f₁=20 cm (P₁=5 D), f₂=-20 cm (P₂=-5 D) in contact, P=0, F infinite, afocal system, beam emerges parallel, principle of corrective lenses for myopia/hypermetropia. Objective magnification: m_o = (L/f_o) = (15/1.25) = 12 . Eyepiece magnification: m_e = (D/f_e) = (25/5) = 5 . Total magnification: m = m_o × m_e = 12 × 5 = 60 . Substituting values gives 60, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.

Ref: NCERT > Physics Book > Ray Optics > Combination of Lenses and Lens Systems

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Optical Instruments - Simple and Compound Microscope

A telescope has an objective of focal length \( 120 \, \text{cm} \) and an eyepiece of focal length \( 6 \, \text{cm} \)

**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. Magnifying power: m = (f_o/f_e) . f_o = 120 cm , f_e = 6 cm . m = (120/6) = 20 . Substituting values gives 20, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.