#image at infinity

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 simple microscope with a focal length of \( 8 \, \text{cm} \) forms an image at infinity. What is the magnification?

**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. 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 > Optical Instruments - Simple and Compound Microscope

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Thin Lenses - Lens Formula, Magnification and Power

A simple microscope with a focal length of \( 4 \, \text{cm} \) forms an image at infinity. What is the magnification?

**Convex lens image formation**: object beyond 2F (u>2f) real inverted diminished between F and 2F, at 2F same size at 2F, between F and 2F magnified beyond 2F, at F image at infinity, within F virtual erect magnified same side. For f=15 cm, u=30 cm=2f, m = v/u =30/30=1? Actually v=30 cm, m=-1, same size inverted. Magnification at infinity: m = (D/f) . D = 25 cm , f = 4 cm . m = (25/4) = 6.25 . Substituting values gives 6.25, 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 > Thin Lenses - Lens Formula, Magnification and Power

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Thin Lenses - Lens Formula, Magnification and Power

A simple microscope with a focal length of \( 6 \, \text{cm} \) forms an image at infinity. What is the magnification?

**Convex lens image formation**: object beyond 2F (u>2f) real inverted diminished between F and 2F, at 2F same size at 2F, between F and 2F magnified beyond 2F, at F image at infinity, within F virtual erect magnified same side. For f=15 cm, u=30 cm=2f, m = v/u =30/30=1? Actually v=30 cm, m=-1, same size inverted. Magnification at infinity: m = (D/f) . D = 25 cm , f = 6 cm . m = (25/6) ≈ 4.167 . Substituting values gives 4.17, 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 > Thin Lenses - Lens Formula, Magnification and Power

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