A professor reads a greeting card received on his 50 th birthday using +2.5 D glasses, holding the card 25 cm away. Ten years later, he reads his farewell letter using the same glasses, but he must hold the letter 50 cm away. Determine the power of the lens he should now use.

Step-by-step solution

Using the lens formula in terms of power, P = 1 v - 1 u . At age 60 , the professor uses the same glasses with power P = +2.5 D to read the letter at a distance u = -50 cm = -0.5 m . The image is formed at his new near point v . Substituting the values to find the vergence of his near point: 1 v = P + 1 u 1 v = 2.5 + ( 1 -0.5 ) 1 v = 2.5 - 2.0 = 0.5 D To read at the normal near point distance of 25 cm ( u' = -25 cm = -0.25 m ), the new lens must form an image at this same near point v . Let the new power required b