Ray Optics and Optical InstrumentsNEET Physics · Class 12 · NCERT Chapter 9

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• Slide the object inside the focal length on a concave mirror: image jumps behind the mirror, virtual and magnified.
• Convex mirror always gives a virtual, erect, diminished image regardless of object position.
• Drag object to u = 2f for concave: image is at the same point, same size, inverted (m = -1).
• When object is at the focal point of a concave mirror, image goes to infinity (parallel reflected rays).

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• Object beyond C (|u| > |2f|): image is between F and C, real, inverted, diminished.
• Object at C (u = 2f): image at C, real, inverted, same size (m = -1).
• Object between F and C: image beyond C, real, inverted, magnified.
• Object at F: image at infinity (rays parallel after reflection).
• Object inside F (|u| < |f|): image virtual, erect, magnified, same as a shaving mirror.

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• Going from rarer to denser: bends towards the normal.
• Going from denser to rarer: bends away from the normal. Past the critical angle: TIR.
• For air-water (n = 1.33), critical angle ≈ 49°. For glass-air (n = 1.5), it is about 42°.
• When θ_1 = 0 (along the normal), the ray passes straight through, no bending.

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• TIR is responsible for the total reflection in optical fibres and prismatic binoculars.
• Diamond has a high n (2.42), so its critical angle is only 24.4°. Most rays hitting an internal facet undergo TIR. Hence the "fire".
• Apparent shimmering of mirages on a hot road: hot air near the surface acts like a denser-to-rarer interface, leading to TIR of light from the sky.
• TIR only happens going denser to rarer. Going rarer to denser, all light refracts in (no TIR).

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• A pool that looks 1 m deep is actually about 1.33 m: divide by n.
• A coin at the bottom of a glass of water seems closer to the surface than its real depth.
• Stick partly in water looks bent at the surface for the same reason.
• Apparent shift = d (1 - 1/n). Used by NEET to ask for shift, not depth itself.

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• A symmetric biconvex lens with |R_1| = |R_2| = R: f = R / (2(n - 1)). For n = 1.5 and R = 20 cm, f = 20 cm.
• Converging lens: positive f. Diverging lens: negative f.
• A planoconvex lens has R_1 = ∞ on the flat side. Then 1/f = (n - 1)(0 - 1/R_2). With R_2 = -R, f = R/(n-1).
• Power in diopters = 1 / f(in metres). A 2 D lens has f = 50 cm.

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• Convex lens, object at 2F: image at 2F on the other side, same size, inverted.
• Object inside F of a convex lens: virtual, erect, magnified, basis of a magnifying glass.
• Concave lens always gives a virtual, erect, diminished image (between optical centre and F on same side).
• Power P (in diopters) = 1 / f(in metres). A camera lens with f = 50 mm has P = 20 D.

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• Convex (+15 cm) + concave (-25 cm) in contact: 1/f = 1/15 - 1/25 = 0.027 → f = 37.5 cm. Net converging, weaker.
• Two equal-power convex lenses in contact: equivalent power doubles, focal length halves.
• A convex and concave lens of equal magnitude (e.g. +15 and -15) in contact give zero power. f = ∞.
• In a compound microscope, the eyepiece and objective are separated; use the d term, not the contact version.

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• Slide i_1 until δ stops decreasing: that is δ_m. There i_1 = i_2 and the ray inside is parallel to the base.
• Crown glass prism A = 60°, n = 1.5: δ_m ≈ 37.2°. Use the prism formula to compute n directly.
• For very thin prisms (A < 10°), δ ≈ (n - 1) A is exact enough.
• A higher n (denser prism) deviates light more for the same A.

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• Compound microscope: pick small f_o (objective close to specimen) and small f_e (high eyepiece power) for max M.
• Telescope: long f_o, short f_e. A 100 cm objective with 5 cm eyepiece gives M = 20×.
• Simple magnifying glass with f = 5 cm: M_D = 1 + 25/5 = 6× (image at near point).
• Compound microscope tube length L is roughly the distance the objective image is formed from the objective lens.