“The medium is bound by two transparent and curved homogenous medium atleast one surface is called the lens.” Curved surface may be spherical, cylindrical or parabolic. Generally the curved surface is spherical. Mainly the lenses are of two types :
(1) Convex lens and
(2) Concave lens.
1. Convex lens: The lenses which are thinner at the edges and thicker at the centre, are called convex lenses. It converges a parallel beam of light on refraction through it. It has a real focus.
Types of Convex Lenses :
(i) Double convex or biconvex lens : In this lens, both surfaces are convex [fig],
(ii) Plano-convex lens : In this lens, one surface is convex and other surface is plane [fig],
(iii) Concavo-convex lens: In this lens, one surface is concave and the other surface is convex [fig],
2. Concave lens : It is thinner at the centre and thicker at the edges. It diverges a parallel beam of light on refraction through it. It has a virtual focus.
Types of Concave Lenses :
(i) Double concave or biconcave lens : In this lens, both sides are concave [fig].
(ii) Plano-concave lens : In this lens, one side is plane and the other is concave [fig],
(iii) Convexo-concave lens : In this lens, one side is convex and the other is concave [fig].
Converging action of convex lens and diverging action of concave lens:
Convex lens bends the parallel rays incident on it towards the principal axis and centralises them at a point, therefore it is called ‘Convergent Lens’ also, on the other hand the concave lens shifts the parallel rays incident on it away from the principal axis i.e., spreads them, therefore it is called ‘Divergent Lens’ also.
When the medium on both sides of the lens is the same : In figure 11.30 a thin lens is shown on both side of which there is the same medium air. The radii of curvature of both the surfaces of the lens are R1 and R2 respectively. The image of a point object O, situated at the principal axis, is formed as I’ by refraction through surface AP1B and the image of virtual object I’ is formed as I, the final image by refraction through second surface AP2B of the lens.
The image I’ formed by first surface behaves as virtual object for second surface and the final image is formed as I, therefore for refraction through second surface of the lens,
because the distance of J’ from the second surface is (v’ – t) where t is the thickness of the lens.
This is called ‘Lens Maker’s Formula’.
In general, the equation (4) can be written as under,
This is known as lens maker formula.
If the lens is placed in a liquid e.g., in water, then the focal length of lens in water fw will be obtained by,
