Question

A 35-year-old patent clerk needs glasses of 50-cm focal length to read patent applications that he holds 25 cm from his eyes. Five years later, he notices that while wearing the same glasses, he has to hold the patent applications 40 cm from his eyes to see them clearly.

What should be the focal length of new glasses so that he can read again at 25 cm?

Answer 1

The focal length of new glasses so that he can read again at 25 cm which will be given as :

To find the new near point, we have

1 / d_o1 + 1 / d_i1 = 1 / f₁                                               { eq.1 }

where, d_o1 = object distance from his eyes = 40 cm

d_i1 = image distance = ?

f₁ = focal length of glasses = 50 cm

inserting the values in eq.1,

1 / (40 cm) + 1 / d_i1 = 1 / (50 cm)

1 / d_i1 = 1 / (50 cm) - 1 / (40 cm)

1 / d_i1 = - (1 / 200) cm

d_i1 = - 200 cm

To give him a normal near point, we have

1 / d_o2 + 1 / d_i2 = 1 / f₂                                                           { eq.2 }

where, d_o2 = new object distance from his eyes = 25 cm

d_i2 = image distance = - 200 cm

inserting these values in eq.2,

1 / (25 cm) + 1 / (-200 cm) = 1 / f₂        

1 / f₂ = (7 / 200) cm

f₂ = 28.5 cm