Grade 12th · Physics · Ray Optics and Optical Instruments
Comprehensive formula cheat sheet and derivations for Class 12 Physics Ray Optics (NCERT Chapter 9). Lens Maker's formula, Prism formula, spherical surface refraction, compound microscope, and astronomical telescope magnification.
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For a spherical interface separating two media of refractive indices μ₁ and μ₂, Snell's law in the paraxial approximation yields: μ₂/v - μ₁/u = (μ₂ - μ₁)/R. Applying this relation consecutively to both faces of a thin lens with radii R₁ and R₂ leads directly to the Lens Maker's Formula: 1/f = (μ₂/μ₁ - 1)(1/R₁ - 1/R₂). When the surrounding medium is air (μ₁ = 1), 1/f = (μ - 1)(1/R₁ - 1/R₂).
When monochromatic light passes symmetrically through a triangular glass prism of angle A, i = e and r₁ = r₂ = A/2. At the position of minimum deviation, deviation δ = δ_m. Applying Snell's law at the first interface gives μ = sin(i) / sin(r) = sin((A + δ_m)/2) / sin(A/2). For a thin prism (A < 10°), this simplifies to δ = (μ - 1)A.
1. Compound Microscope: Designed to magnify micro specimens. Objective lens has short focal length (f_o) and small aperture; eyepiece has moderate focal length (f_e) and larger aperture. Magnifying power at near point (D = 25cm): m = -(L/f_o)(1 + D/f_e). At infinity (relaxed eye): m = -(L/f_o)(D/f_e). 2. Astronomical Telescope: Designed for celestial viewing. Objective lens has large focal length (f_o) and large aperture (to gather light); eyepiece has small focal length (f_e). In normal adjustment (image at infinity): m = -f_o/f_e and length of tube L = f_o + f_e.
When light travels from an optically denser medium (refractive index μ) to an optically rarer medium (air) at an angle of incidence greater than the critical angle (i > C), the entire ray is reflected back into the denser medium. Critical angle condition: sin(C) = 1/μ. Applications include optical fibers (core μ₁ > cladding μ₂), diamond brilliance, and totally reflecting right-angled prisms.
Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.
Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.
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The Lens Maker's formula is 1/f = (μ - 1)(1/R₁ - 1/R₂), where f is the focal length, μ is the relative refractive index of the lens material, and R₁ and R₂ are the radii of curvature of the two lens surfaces.
In normal adjustment (final image at infinity), m = -f_o / f_e, and the tube length is L = f_o + f_e. When the final image is formed at the least distance of distinct vision (D), m = -(f_o / f_e) × (1 + f_e / D).
Since the relative refractive index (μ_glass / μ_water = 1.5 / 1.33 = 1.128) is much smaller than in air (1.5), (μ - 1) decreases, causing the focal length f to increase to approximately 4 times its value in air.