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#curvature radius

2 public questions tagged with this topic.

A double convex lens has radii of curvature \( 20 \, \text{cm} \) each and refractive index \( 1.5 \). What is its focal

**Telescope resolving power** depends on objective aperture, magnification limited by objective diffraction, terrestrial telescope adds erecting lens, Galilean uses diverging eyepiece for erect image, reflecting telescope uses concave mirror objective avoiding chromatic aberration. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.5 , R₁ = 20 cm , R₂ = -20 cm (sign convention). (1/f) = (1.5 - 1) ( (1/20) - (1/-20) ) = 0.5 ( (1/20) + (1/20) ) = 0.5 × (2/20) = (1/20) . f = 20 cm . Substituting values gives 20 cm, which matches expected image position and magnification from mirror

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

A double convex lens of refractive index \( 1.5 \) has radii of curvature \( 15 \, \text{cm} \) and \( -15 \, \text{cm}

**Lens maker's formula** 1/f = (n-1)(1/R₁ - 1/R₂), n refractive index, R₁,R₂ radii of curvature (m), sign convention R positive if surface convex towards incident light. For double convex R₁=12 cm, R₂=-12 cm, n=1.5, 1/f=(0.5)(1/12 -1/(-12))=(0.5)(2/12)=1/12, f=12 cm, converging. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.5 , R₁ = 15 cm , R₂ = -15 cm . (1/f) = (1.5 - 1) ( (1/15) - (1/-15) ) = 0.5 ( (1/15) + (1/15) ) = 0.5 × (2/15) = (1/15) . f = 15 cm . Substituting values gives 15 cm, which matches expected image

Ref: NCERT > Physics Book > Ray Optics > Refraction at Spherical Surfaces and Lens Maker's Formula