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Thermodynamics

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Principal Foci

In the equation if the object is at infinity then, u = ∞ and

Let ƒ₁ be the value of v corresponding to u = ∞.

This values of v = ƒ₂ is termed as the second principal focal length and the position of the image corresponding to the object at infinity is called the second principal focus of the refracting surface.

Similarly, if v = ∞, i.e. the object is so placed that the refracted rays become parallel to the principal axis, then

This value of u is called the first principal focal length of the refracting surface and is denoted by ƒ₁ and the position of the axial point object, whose image is formed at infinity is known as the first principal focus of the refracting surface.

From equations (ii) and (i)

As and are always positive and unequal, ƒ₁ and ƒ₂ are always unequal and of opposite sign.

Substituting the values of

This formula holds good only for paraxial rays.