how to apply lense makers formula.i mean to say which one of the radii is taken first and which one after that.for example in this question.calculate the focal length of a concave lens in water(r.f of water is 4/3)if the surfaces have radii equal to 40cm & 30 cm.R.F of glass is 1.5

Dear student,

It is a relation that connects focal length of a lens to radii of curvature of the two surfaces of the lens and refractive index of the material of the lens.

The following assumptions are made for the derivation:

• The lens is thin, so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centre of the lens.

• The aperture of the lens is small.

• Point object is considered.

• Incident and refracted rays make small angles.

Consider a convex lens (or concave lens) of absolute refractive index m₂ to be placed in a rarer medium of absolute refractive index m₁.

Considering the refraction of a point object on the surface XP₁Y, the image is formed at I₁ who is at a distance of V₁.

CI₁= P₁I₁ = V₁ (as the lens is thin)

CC₁ = P₁C₁ = R₁

CO = P₁O = u

It follows from the refraction due to convex spherical surface XP₁Y

The refracted ray from A suffers a second refraction on the surface XP₂Y and emerges along BI. Therefore I is the final real image of O.

Here the object distance is

(Note P₁P₂ is very small)

(Final image distance)

Let R₂ be radius of curvature of second surface of the lens.

\ It follows from refraction due to concave spherical surface from denser to rarer medium that

Adding (1) & (2)

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All the best.

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