THIN LENS

Consider the thin lens shown here with the two refracting surfaces having radii of curvature equal to R1 and R2 respectively. The refractive indices of this surrounding medium and of the material of the lens are μ₁ and  μ₂ respectively

EQUIVALENT FOCAL LENGTH OF TWO OR MORE THIN LENSES IN CONTACT

F^-1 = (f^-1)₁  + (f^-1)_{2 +} (f^-1)_{3 + ...}

Special cases

(a)    If the lens is immersed in a liquid whose refractive index is greater than refractive index of material of the lens then

Note:    A lens is converging if its focal length is positive and diverging if focal length is negative (in neo-Cartesian sign convention). From this we can conclude that a convex lens need not necessarily be a converging and a concave lens diverging.

Ray Tracing for Lens:

Illustration 6:    A glass rod has ends as shown in figure, The refractive index of glass is μ. The object point O is at a distance 2R from the surface of larger radius of curvature. The distance between the apexes of the ends is 3R. Show that the image point of O is formed at a distance of

(9 - 4μ)R / (10μ - 9)(μ-2)

Solution:    From the right hand vertex.