For a normal eye, the far point is at infinity and the near point of distinct vision is about 25cm in front of the eye. The cornea of the eye provides a converging power of about 40 dioptres, and the least converging power of the eye-lens behind the cornea is about 20 dioptres. From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye-lens) of a normal eye.


Given:


Least distance of distinct vision, d = 25 cm
Far point of a normal eye, d’ = ∞
Converging power of the cornea,
Least converging power of the eye-lens, Pc = 40D
To see the objects at infinity, the eye uses its least converging power.
Power of the eye-lens, P = Pc + Pe = 40 + 20 = 60D


Power of the eye-lens is given as:


P = 1/ focal length


f = 1/P × 1/60D


100/60 = 5/3cm
To focus an object at the near point, object distance (u) = −d = −25 cm
Focal length of the eye-lens = Distance between the cornea and the retina = Image
distance
Hence, image distance, v = 53
Applying the lens formula we have:


…(1)


Where, f0 = focal length of the objective lens


v0 = Distance of image formation


u0 = Distance of object from objective


1/f = 3/5 + 1/25


1/f = (15 + 1)/25 = 16/25cm-1


Power P’ = 1/f′ × 100


P = 16/25 × 100 = 64D


Therefore Power of the eye-lens = 64 − 40 = 24 D
Hence, the range of accommodation of the eye-lens is from 20D to 24D


24
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