Equivalent Focal Length Of Thin Lenses In Contact — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Equivalent Focal Length of Thin Lenses in Contact Applies to two or more thin lenses placed in direct contact coaxially (sharing the same principal axis) without any separation distance. Consider an object O placed on the principal axis of the first lens. The first lens forms an image I1 at distance v1: 1/v1 - 1/u = 1/f1. The image I1 acts as a virtual object for the second lens. The second lens forms the final image I at distance v: 1/v - 1/v1 = 1/f2. Add the two equations to eliminate 1/v1, resulting in 1/v - 1/u = 1/f1 + 1/f2. Compare with the lens formula for an equivalent lens (1/F = 1/v - 1/u) to obtain 1/F = 1/f1 + 1/f2. Lenses must be thin (thickness is negligible compared to radii of curvature). Distance between optical centers is zero (d=0). Lenses must share the same principal axis. Surrounding medium is uniform. Adding focal lengths directly (F = f1 + f2) instead of adding powers/reciprocals. Ignoring sign conventions (e.g., treating concave lens focal length as positive). Applying this specific formula when there is a separation distance 'd' between lenses (requires -d/f1f2 term). Thinking the order of lenses matters (it does not for thin lenses in contact).