#double convex lens

Telescope, Human Eye and Defects of Vision

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

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens has radii of curvature \( 30 \, \text{cm} \) and \( -30 \, \text{cm} \) with refractive index \( 1.

**Spherical refracting surface** power P = (n₂-n₁)/R, lens power sum of two surfaces. Lens maker derivation combines two refractions, sign of R₂ negative for second surface convex opposite direction, yielding 1/f positive for convex lens. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.6 , R₁ = 30 cm , R₂ = -30 cm . (1/f) = (1.6 - 1) ( (1/30) - (1/-30) ) = 0.6 ( (1/30) + (1/30) ) = 0.6 × (2/30) = (1.2/30) = (1/25) . f = 25 cm . Substituting values gives 25 cm, which matches expected image position and

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.5 \) has radii of curvature \( 18 \, \text{cm} \) and \( -18 \, \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 = 18 cm , R₂ = -18 cm . (1/f) = (1.5 - 1) ( (1/18) - (1/-18) ) = 0.5 ( (1/18) + (1/18) ) = 0.5 × (2/18) = (1/18) . f = 18 cm . Substituting values gives 18 cm, which matches expected image

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

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.55 \) has radii of curvature \( 22 \, \text{cm} \) and \( -22 \, \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 = 1.55 , R₁ = 22 cm , R₂ = -22 cm . (1/f) = (1.55 - 1) ( (1/22) - (1/-22) ) = 0.55 ( (1/22) + (1/22) ) = 0.55 × (2/22) = (1.1/22) = (1/20) . f = 20 cm . Substituting values gives 20 cm, which matches

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Refraction at Spherical Surfaces and Lens Maker's Formula

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

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.5 \) has radii of curvature \( 40 \, \text{cm} \) and \( -40 \, \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 = 40 cm , R₂ = -40 cm . (1/f) = (1.5 - 1) ( (1/40) - (1/-40) ) = 0.5 ( (1/40) + (1/40) ) = 0.5 × (2/40) = (1/40) . f = 40 cm . Substituting values gives 40 cm, which matches expected image

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.55 \) has radii of curvature \( 30 \, \text{cm} \) and \( -30 \, \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 = 1.55 , R₁ = 30 cm , R₂ = -30 cm . (1/f) = (1.55 - 1) ( (1/30) - (1/-30) ) = 0.55 ( (1/30) + (1/30) ) = 0.55 × (2/30) = (1.1/30) . f = (30/1.1) ≈ 27.27 cm . Substituting values gives 27.3 cm, which matches

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.6 \) has radii of curvature \( 25 \, \text{cm} \) and \( -25 \, \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 = 1.6 , R₁ = 25 cm , R₂ = -25 cm . (1/f) = (1.6 - 1) ( (1/25) - (1/-25) ) = 0.6 ( (1/25) + (1/25) ) = 0.6 × (2/25) = (1.2/25) . f = (25/1.2) ≈ 20.83 cm . Substituting values gives 20.8 cm, which matches

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Refraction at Spherical Surfaces and Lens Maker's Formula

A double convex lens of refractive index \( 1.5 \) has radii of curvature \( 12 \, \text{cm} \) and \( -12 \, \text{cm}

**Spherical refracting surface** power P = (n₂-n₁)/R, lens power sum of two surfaces. Lens maker derivation combines two refractions, sign of R₂ negative for second surface convex opposite direction, yielding 1/f positive for convex lens. Lens maker’s formula: (1/f) = (n - 1) ( (1/R₁) - (1/R₂) ) . n = 1.5 , R₁ = 12 cm , R₂ = -12 cm . (1/f) = (1.5 - 1) ( (1/12) - (1/-12) ) = 0.5 ( (1/12) + (1/12) ) = 0.5 × (2/12) = (1/12) . f = 12 cm . Substituting values gives 12 cm, which matches expected image position and magnification from

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