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#lens calculation

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Refraction at Plane Surfaces and Snell's Law

A lens has a power of \( +4 \, \text{D} \). What is its focal length in centimeters?

**Snell's law** n₁ sinθ₁ = n₂ sinθ₂ describes refraction at plane interface, n refractive index, θ angle with normal. When light goes from denser n=1.52 glass to rarer air n=1, sinθ₂ = (n₁/n₂) sinθ₁ > sinθ₁, bending away from normal, enabling total internal reflection beyond critical angle. Power: P = (1/f) (in meters). P = +4 D ⇒ 4 = (1/f) ⇒ f = (1/4) = 0.25 m = 25 cm . Substituting values gives 25 cm, 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 Plane Surfaces and Snell's Law

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Refraction at Plane Surfaces and Snell's Law

A concave lens of focal length \( 25 \, \text{cm} \) has an object placed \( 50 \, \text{cm} \) from it. What is the ima

**Refraction at plane surface** changes direction due to speed change v = c/n, n = c/v. For water n=1.33 to air, n₁>n₂, ray bends away, if θ₁ > C, sinθ₂>1 impossible, TIR occurs. Snell's law quantitative prediction of θ₂ from θ₁ and indices. Focal length: f = -25 cm (concave lens). Object distance: u = -50 cm . Lens formula: (1/v) - (1/u) = (1/f) . (1/v) - (1/-50) = (1/-25) ⇒ (1/v) + (1/50) = (1/-25) ⇒ (1/v) = (1/-25) - (1/50) = (-2 - 1/50) = (-3/50) . v = -(50/3) ≈ -16.67 cm (virtual image). Substituting values gives 16.7 cm, which matches

Ref: NCERT > Physics Book > Ray Optics > Refraction at Plane Surfaces and Snell's Law

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