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#lens equation

2 public questions tagged with this topic.

Refraction at Spherical Surfaces and Lens Maker's Formula

A concave lens of focal length \( 10 \, \text{cm} \) forms an image \( 5 \, \text{cm} \) from the lens. What is the obje

**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. Focal length: f = -10 cm (concave lens). Image distance: v = -5 cm (virtual image). Lens formula: (1/v) - (1/u) = (1/f) . (1/-5) - (1/u) = (1/-10) ⇒ (1/u) = (1/-5) - (1/-10) = (-2 + 1/10) = (-1/10) . u = -10 cm . Substituting values gives 10 cm, which matches expected image position and magnification from mirror/lens f

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 convex lens of focal length \( 10 \, \text{cm} \) forms an image at \( 20 \, \text{cm} \) from the lens. What is the o

**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. Focal length: f = 10 cm . Image distance: v = 20 cm (real image). Lens formula: (1/v) - (1/u) = (1/f) . (1/20) - (1/u) = (1/10) ⇒ (1/u) = (1/20) - (1/10) = (1 - 2/20) = (-1/20) . u = -20 cm . Substituting values gives 20 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u

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

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