#magnification

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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Combination of Lenses and Lens Systems

A simple microscope with a lens of focal length \( 10 \, \text{cm} \) forms an image at the least distance of distinct v

**Combination of lenses in contact** effective power P = P₁+P₂, effective focal length 1/F = 1/f₁ + 1/f₂, for thin lenses in contact. If separated by d, 1/F =1/f₁+1/f₂ - d/(f₁ f₂). Power adds algebraically, converging + with diverging - can cancel, used to correct aberrations and design achromatic doublets. Magnification: m = 1 + (D/f) . D = 25 cm , f = 10 cm . m = 1 + (25/10) = 1 + 2.5 = 3.5 . Substituting values gives 3.5, 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

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

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Combination of Lenses and Lens Systems

An object is placed \( 15 \, \text{cm} \) from a convex mirror of focal length \( 30 \, \text{cm} \). What is the magnif

**Combination of lenses in contact** effective power P = P₁+P₂, effective focal length 1/F = 1/f₁ + 1/f₂, for thin lenses in contact. If separated by d, 1/F =1/f₁+1/f₂ - d/(f₁ f₂). Power adds algebraically, converging + with diverging - can cancel, used to correct aberrations and design achromatic doublets. Focal length: f = 30 cm , u = -15 cm . Mirror equation: (1/v) + (1/-15) = (1/30) ⇒ (1/v) = (1/30) + (1/15) = (1 + 2/30) = (3/30) = (1/10) . v = 10 cm . Magnification: m = -(v/u) = -(10/-15) = 0.67 . Substituting values gives 0.67, which matches expected

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

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Combination of Lenses and Lens Systems

In a simple microscope, why is the image formed larger when the object is placed closer to the lens than the focal point

**Lens combination** effective focal length calculation uses reciprocal sum, for f₁=10 cm, f₂=20 cm in contact, 1/F=1/10+1/20=3/20, F=6.67 cm, P=15 D, stronger converging than either alone, illustrating power addition. In a simple microscope, placing the object between the lens and focal point results in a virtual, erect, and magnified image. The closer the object is to the lens (inside F), the greater the divergence of rays, increasing the apparent size of the virtual image seen by the observer. Substituting values gives Due to increased divergence of rays, 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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Refraction at Spherical Surfaces and Lens Maker's Formula

A simple microscope uses a lens of focal length \( 8 \, \text{cm} \). What is the magnification when the image is at inf

**Refraction at spherical surface** formula n₁/u + n₂/v = (n₂-n₁)/R governs single surface, extension to two surfaces yields lens maker. Double convex with equal |R| has f = R/[2(n-1)], for R=12 cm, n=1.5, f=12 cm, illustrating dependence on curvature and index. Magnification at infinity: m = (D/f) . D = 25 cm , f = 8 cm . m = (25/8) = 3.125 . Substituting values gives 3.1, 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 > Refraction at Spherical Surfaces and Lens Maker's Formula

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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.