Question

How will you calculate the focal length of a biconvex lens that is used to correct the defect of Hypermetropia? Explain it mathematically.

Answer 1

Hypermetopia :- A long sighted eyes can see distant objects clearly but nearer objects are not clear visible .

it means Person who face this defect
see clearly of object placed in infinite .
e.g u = -∞ ( negative sign indicate object placed left side of lens )

use formula,
1/v - 1/( -∞) = 1/f

v = f

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calculation of focal length of lens
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we know, eyes see clearly when object placed minimum = 25 cm
hence , u = -25 cm (negative sign indicate object placed left side of lens )

let D is the nearest sightness for hypermetropia eyes .
e.g v = -D cm

now ,
use lens formula,

1/v - 1/u = 1/f

1/(-D) - 1/( -25 ) = 1/f

1/f = 1/25 - 1/D

=(D - 25)/25D

f = 25D/(D -25 ) cm

let D = 100 cm

then focal length ( f ) = 2500/75 =100/3 cm

Answer 2

Hypermetropia is also known as Far sightedness.
A person suffering with this defect cannot see objects at near distance but can see objects at far distance.
To calculate focal length:
Let us consider the object is at point of Least distance of distinct vision.(L)
Defect of Hypermetropia defect can be corrected when image of object at L is formed at the near point (H) by using convex lens.
object distance = u= -25cm
Image distance= V=distance of near point= -d
Let f be the focal length of biconvex lens
by using Lens Formula:
1/f = 1/ v - 1/ u
1/ f = 1/ (-d) - 1/(-25)
1/ f = -1/ d + 1/ 25
1/f = ( d-25)/ 25d
Therefore
f= 25d/(d-25)