Question

Obtain lens maker’s formula and mention its significance.

Answer 1

Lens maker’s formula and lens equation: 

Let us consider a thin lens made up of a medium of refractive index n₂ , is placed in a medium of refractive index n₁. Let R₁ and R₂ be the radii of curvature of two spherical surfaces (1) and (2) respectively and P be the pole. Consider a point object O on the principal axis. The ray which falls very close to P, after refraction at the surface (1) forms image at I’. Before it does so, it is again refracted by the surface (2). Therefore the final image is formed at I. The general equation for the refraction at a spherical surface is given by

For the refracting surface (1), the light goes from n₁ to n₂.

For the refracting surface (2), the light goes from medium n₂ to n₁.

Adding the above two equation (1) and (2)

If the object is at infinity, the image is formed at the focus of the lens. Thus, for u = ∞, v= f. Then the equation becomes.

If the refractive index of the lens is and it is placed in air, then n₂ = n and n₁ = 1 equation (4) becomes,

The above equation is called the lens maker’s formula, because it tells the lens manufactures what curvature is needed to make a lens of desired focal length with a material of particular refractive index. This formula holds good also for a concave lens. By comparing the equations (3) and (4) we can write,

This equation is known as lens equation which relates the object distance u and image distance v with the focal length f of the lens. This formula holds good for a any type of lens.