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#converging beam

5 public questions tagged with this topic.

Refraction at Spherical Surfaces and Lens Maker's Formula

A converging beam meets a concave lens (\( f = 20 \, \text{cm} \)) \( 5 \, \text{cm} \) before the convergence point. Wh

**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. Object distance: u = -5 cm (virtual object), f = -20 cm . Lens formula: (1/v) - (1/-5) = (1/-20) ⇒ (1/v) + (1/5) = (1/-20) . (1/v) = (1/-20) - (1/5) = (-1 - 4/20) = (-5/20) = (-1/4) . v = -4 cm (4 cm to the left). Substituting values gives 4 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u

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 converging beam meets a concave lens (\( f = 15 \, \text{cm} \)) \( 6 \, \text{cm} \) before the convergence point. Wh

**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. Object distance: u = -6 cm (virtual object), f = -15 cm . Lens formula: (1/v) - (1/-6) = (1/-15) ⇒ (1/v) + (1/6) = (1/-15) . (1/v) = (1/-15) - (1/6) = (-2 - 5/30) = (-7/30) . v = -(30/7) ≈ -4.29 cm (4.29 cm to the left). Substituting values gives 4.3 cm, which matches expected image position and magnification from mirror/lens

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

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Total Internal Reflection and Critical Angle

A converging beam meets a concave lens (\( f = 20 \, \text{cm} \)) \( 8 \, \text{cm} \) before the convergence point. Wh

**Critical angle** C satisfies sinC = n₂/n₁, n₁>n₂, n₂=1 for air, n₁=1.52 for glass gives sinC=1/1.52=0.6579, C≈41.1°, for water n=1.33 C=48.75°. Beyond C, total internal reflection occurs, all light reflected, no refracted ray, used in optical fibers and prisms. Object distance: u = -8 cm (virtual object), f = -20 cm . Lens formula: (1/v) - (1/-8) = (1/-20) ⇒ (1/v) + (1/8) = (1/-20) . (1/v) = (1/-20) - (1/8) = (-2 - 5/40) = (-7/40) . v = -(40/7) ≈ -5.71 cm (5.71 cm to the left). Substituting values gives 5.7 cm, which matches expected image position and magnification from mirror/lens formula 1/f

Ref: NCERT > Physics Book > Ray Optics > Total Internal Reflection and Critical Angle

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Reflection by Spherical Mirrors and Mirror Formula

A converging beam meets a convex lens (\( f = 12 \, \text{cm} \)) \( 6 \, \text{cm} \) before the convergence point. Wha

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Object distance: u = -6 cm (virtual object), f = 12 cm . Lens formula: (1/v) - (1/-6) = (1/12) ⇒ (1/v) + (1/6) = (1/12) . (1/v) = (1/12) - (1/6) = (1 - 2/12) = (-1/12) . v = -12 cm (12 cm to the left).

Ref: NCERT > Physics Book > Ray Optics > Reflection by Spherical Mirrors and Mirror Formula

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Reflection by Spherical Mirrors and Mirror Formula

A converging beam meets a concave lens (\( f = 10 \, \text{cm} \)) \( 4 \, \text{cm} \) before the convergence point. Wh

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Object distance: u = -4 cm (virtual object), f = -10 cm . Lens formula: (1/v) - (1/-4) = (1/-10) ⇒ (1/v) + (1/4) = (1/-10) . (1/v) = (1/-10) - (1/4) = (-2 - 5/20) = (-7/20) . v = -(20/7) ≈ -2.86 cm (2.86 cm to the left). Substituting values gives 2.86 cm, which

Ref: NCERT > Physics Book > Ray Optics > Reflection by Spherical Mirrors and Mirror Formula

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