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Aplanatic Lens

A spherical lens which is free from the defects of spherical and coma is called an aplanatic lens. A pair of conjugate points free from spherical aberration and coma are called aplanatic points. Fig. illustrates the property of an aplanatic lens. Let O be the centre of the curvature of the lens of refractive index and radius of curvature R. P is a point on the axis of the lens such that . It can be shown that all rays passing through the point P appear to diverge through the point Q irrespective of the slope angle made by the incident rays. PA is the incident ray and AC is the refracted ray. The ray AC appears to diverge from the point Q which is the image of P. Let i and r be the angles of incidence and refraction and and the slope angles made by the incident and refracted rays.

From (i) and (ii)

∴ ∠ = ∠ r                                             (iii)

In the Δ APO,

∠ = + (r – i)                                     (iv)

Substituting ∠ = ∠ r in equation (iv)

r = + r – 1 or i =                                (v)

In the Δ AQO,

OQ = .R

Thus, if the distance of the object point P is R/ from the centre of curvature, then the distance of the image point Q is R irrespective of the slope angles and . The object and image distances of the conjugate points that satisfy the above condition are BP = R + R/ and BQ = R + R.

An aplanatic lens is mostly used as the front lens of a high power microscope objective called the oil immersion objective. As it is not possible to place an object inside a solid spherical lens, the lens is ground a little and the object to be examined is embedded in between a drop of oil and the lens surface. The oil chosen is such that it has the same refractive index as that of the lens.