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