Question

Mrs. Reshmi Singh broke her reading glasses. When she went to the shopkeeper to order new specs, he suggested that she should get spectacles with plastic lenses rather than the glass lenses. When she got 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 a perfect explanation for this. Mrs. Singh raised a similar question to her daughter Anuja at home who explained why the plastic lenses were thicker.
A. Write two qualities displayed each by Anuja and her mother.
B. How do you explain this fact with the help of a lens maker’s formula?

Answer 1

Hint: The lens maker’s equation has to be used here. The reciprocal of the focal length is equivalent to the product of the difference of the refractive indices and the difference of the reciprocal of the radius of curvature of the surfaces of a lens. These all may help you to solve this question.

Complete step-by-step solution:
A. The good quality of Anuja and her mother is that Anuja is very helpful and has deep knowledge in the area of lenses. The mother is very curious even at this age and is very compassionate about the subject.
B. as we all know, the Lens maker’s formula is given in the form of the equation as,
$${\displaystyle \frac{1}{F}}={\mu }_2-{\mu }_1({\displaystyle \frac{1}{R_1}}-{\displaystyle \frac{1}{R_2}})$$
Where $$F$$be the focal length, $${\mu }_2$$ be the refractive index of the lens, $${\mu }_1$$ be the refractive index of the medium where the lens is kept, here it is air. Therefore we can write that,
$${\displaystyle \frac{1}{F}}={\mu }_2-1({\displaystyle \frac{1}{R_1}}-{\displaystyle \frac{1}{R_2}})$$
$$R_1$$ be the radius of curvature of one side, $$R_2$$ be the radius of the other side. As we all know, the refractive index of the glass is higher than the refractive index of plastic, we can write that,
$${\mu }_g>{\mu }_p$$
Therefore the value of the refractive index minus one will also obey this relation.
$${\mu }_g-1>{\mu }_p-1$$
As this value is greater for the glass lens, the focal length of the same will get decreased due to an inverse relationship.
$$F_p>F_g$$
This is why the thickness of a plastic lens is increased to keep the focal length of the lens the same. Therefore the correct answer has been obtained.

Note: Plastic is much lighter than glass. These characteristics make it more comfortable to wear all day and limit the tendency of the glass to slide down your nose. Glass is more resistant than plastic, making the glasses last longer. Plastic lenses are less reflective than glass lenses. This makes them clearer and less prone to glare.