Refraction Through Convex Lens

In fig. AB is the aperture of the lens. Let be the refractive index of the material of the lens. O is an object point on the lens axis and I is the image. Let J K S be the incident spherical wavefront. By the time the disturbance at the points J and S reaches the points P and Q (along the paths J A P and SBQ respectively) the secondary waves from the point K must have travelled a distance KL through the medium of the lens. Therefore, PLQ forms the refracted spherical wavefront whose centre of curvature is I. Hence I is the image of O.

Also, the optical path

OA + AI = OK + KL + LI

= (OM – KM) + (KM + ML) + MI – ML)                (i)

A M B is perpendicular to the axis of the lens.

Here, AM = h

MO = u, MI = v and R₁ and R₂ are the radii of curvature of the first and the second surfaces A K B and ALB of the lens.

In the Δ OAM,

OA₂ = OM₂ + AM₂





Similarly from the Δ AMI

AI² = MI² + AM²

For the spherical surface AKB



And for the spherical surface ALB



Substituting these values in equation (i)

Simplifying equation (vii)



According to the sign convention u is –ve, v is +ve, R₁ is +ve and R₂ is –ve.



If the object is at infinity u = ∞ and v = ƒ

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