What is the primary reason optical fibers can transmit light over long distances with minimal loss?
**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. Optical fibers use total internal reflection to transmit light. The core has a higher refractive index than the cladding, ensuring that light rays striking the boundary at angles greater than the critical angle are fully reflected, preventing loss of light intensity over distance. Substituting values gives Total internal reflection within the core, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v -
Ref: NCERT > Physics Book > Ray Optics > Refraction at Spherical Surfaces and Lens Maker's Formula