Refraction Through Concave Lens

APB and CQD are the two refracting surfaces of a concave lens. O is a point object on the a.. is of the lens. ALB is the incident spherical wavefront whose centre of curvature is O. By the time the disturbance at the points A and B reaches the points C and D, the disturbances at L reaches the point N. CND is the refracted spherical wavefront whose centre of curvature is I. I is the image of O.

The optical paths from A to C and L to N must be equal.

∴ AC = LP + PQ + QN

But, AC = KM (approximately)

∴ KM = LP + PQ + QN

[KP + PQ + QM] = LP + PQ + QN

Or, [KP + QM] = (KP – KL) + (QM + MN)              (i)

Here, AL = CM = h (approximately)



Substituting these values in equation (i)



According to the convention of signs, u is –ve, v is –ve R₁ is –ve and R₂ is +ve



If, u = ∞, v = ƒ

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