Optical Instruments

Simple Magnifier (Convex Lens) A single convex lens used close to the eye, with the object placed within the focal length. Magnification at near point D = 25 cm: M = 1 + D/f. Magnification at infinity (relaxed eye): M = $\frac{D}{f}$. The image at D gives slightly higher magnification. Used in: jeweler's loupe, watchmaker's glass, reading glass.

Compound Microscope Two-lens system for very high magnification of small nearby objects. Objective lens (short focal length $f_o$) forms a real, inverted, magnified intermediate image just inside the eyepiece. Eyepiece (longer focal length $f_e$) acts as a simple magnifier for this intermediate image. At infinity: M = −\frac{L}{f_o}$$\frac{D}{f_e}, where L = distance from back focal point of objective to front focal point of eyepiece (tube length). Tube length approximately L + $f_e$. The negative sign confirms the final image is inverted. To increase magnification: decrease both $f_o$ and $f_e$.

Astronomical (Refracting) Telescope For viewing distant objects. Objective (long $f_o$) forms a real, inverted, diminished image at its focal plane. Eyepiece (short $f_e$) magnifies this intermediate image. Normal adjustment (image at ∞, relaxed eye): M = −$f_o$/$f_e$; tube length L = $f_o$ + $f_e$. For image at near point D: M = −$\frac{f_o}{f_e}$(1 + $f_e$/D). To increase magnification: increase $f_o$ or decrease $f_e$.

KEY DISTINCTION: Microscope objective → SHORT focal length. Telescope objective → LONG focal length. This is opposite and is frequently tested in NEET.

Human Eye and Defects

The human eye has a variable focal length (accommodation) allowing it to focus from 25 cm (near point D) to infinity (far point). The crystalline lens adjusts its curvature via ciliary muscles.

Myopia correction formula: Lens must form virtual image of object at ∞ at the patient's far point (distance d): P = −1/d (d in metres).

Hypermetropia correction: Lens forms virtual image of object at normal near point (25 cm) at the patient's near point (distance $n_p$): use lens formula with u = −25 cm, v = −$n_p$ cm.

Applications of TIR

• Optical fibres: data and internet transmission; endoscopes for medical imaging.
• Diamond cutting: facets designed to exceed θ_c = 24.4°, maximizing internal TIR for brilliance.
• Totally reflecting prisms: used in binoculars and periscopes (100% reflection, no absorption).
• Mirage: TIR of sky light in hot desert air gradients, appearing as a pool of water.
• Retroreflectors: used on roads and satellites for precise ranging.