Q23
Mrs. Rashmi Singh broke her reading glasses. When she went to the shopkeeper to order new spects, he suggested that she should get spectacles with plastic lenses instead of glass lenses. On getting the new spectacles, she found that the new ones were thicker than the earlier ones, she asked this question to the shopkeeper but he could not offer satisfactory explanation for this. At home, Mrs. Singh raised the same question to her daughter Anuja who explained why plastic lenses were thicker.
(a) Write two qualities displayed each by Anuja and her mother.
(b) How do you explain this fact using lens maker’s formula ?
Solution
(b) According to lens maker’s formula,
1/f=(n-1)(1/R₁-1/R₂)
where f is the focal length, n is the refractive index and R₁ and R₂ is the radius of curvature of the lens.
Since, ng > np where g stands for glass and p stands for plastic. Therefore, we get (ng -1) > (np -1).
By lens maker’s formula, we know that focal length is inversely proportional to (μ -1).
Hence, fp > fg.
Thus, in the case of plastic lens, the thickness of the lens should be increased to keep the same focal length as that of the glass lens to give the same power.