Question

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?

Answer 1

(a) Two qualities displayed by Anuja are awareness and explainer and Mrs. Rashmi Singh are curious and observant. 

(b) The lens maker formula is given as `1/f = ( μ−1 ) (1/R_1− 1/R_2)`
where f is the focal length, μ is the refractive index and R1 and R2 is the radius of curvature of the lens.
Since μg > μp

where, g stands for glass and p stands for plastic.

Therefore, we get (μ_g−1) > (μ_p−1)

Now, using the lens maker formula, we see that focal length is inversely proportion to (μ−1)

Hence, f_p > f_g

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.