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#focal length calculation

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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

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 \( 1.5 \) 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

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

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