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

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

Express your answer to two significant figures and include the appropriate units.

Explanation:

In the second case , he wants that object placed at 40 cm be visible . For it he should wear a spec which forms image of object such  that rays  coming from 25 cm  appear  coming from 40 cm . In other words

object distance u = 25 cm

image distance v = 40 cm

f = ?

Both u and v are negative as both are in front of lens.

applying lens formula

1 / v - 1 / u = 1 /f

- 1 / 40 + 1 /25 = 1 /f

= 15 / (40 x 25 )  = 1 / f

f = (40 x 25 ) / 15

= 66.67 cm

= 67 cm

scientific laws are the result of testing theories and proving them to be facts.