# Hygen’s Eyepiece consist of two Plano convex lenses L1&L2 of same material having focal length +3f & +f

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Hygen’s Eyepiece consist of two Plano convex lenses L1&L2 of same material having focal length +3f & +f separated by a distance d from each other. Their convex side face the incident light. Hygen’s’ Eyepiece is achromatic when lenses are placed coaxially at distance

a) d=f /2

b) d=f

c) d=2f

d ) d=3f

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Correct option is c) d = 2f

Explanation:

As we know that in case of Achromatism by separated doublet separation distances between two lenses is given by : d = (ω1f1+ ω2f2)/ (ω12

In case when lenses are of same material, ω1 = ω2 = ω Then d = (f1+f2)/2 in this problem f1=3f & f2=f

d = (f1+f2)/2=3f+f/2=2f

Hygen’s Eyepiece satisfies the condition of Achromatism and has the same focal length for all colours. This makes Hygen’s Eyepiece apparently free from lateral chromatic aberration.