Question

The optical prescription of a pair of spectacle is
Right eye is: \[ - 3.5\;{\rm{D}}\] left eye: \[ - 4.00\;{\rm{D}}\]
i) Name the defect of the eye
ii) Are these lenses thinner at the middle or at the edges?
iii) Which lens has a greater focal length?

Answer 1

Hint: The above problem can be resolved using the concept and application of the power of the lens. The power of lens widely decides the type of lens undertaken for the purpose. Along with this, the mathematical relation for the power and focal length of the lens is also utilised to conclude.

Complete step by step answer:
Given:
The power of the lens of the Right eye is, \[{P_1} = - 3.5\;{\rm{D}}\].
The power of the lens of the left eye is, \[{P_2} = - 4.00\;{\rm{D}}\].
i) From the given information, it is clear that the lenses have the negative sign convention for the powers and this means the person is nearsighted or he/she cannot be able to see the nearby objects. Therefore, the person is having Myopia as an eye defect.
ii) From the given details, as the powers of the lens are negative and this makes the focal length of the lens also negative. And the lenses having the negative convention for the focal length are known as the concave lenses. And the concave lenses are thinner in the middle.
iii) The mathematical formula for the power of lens is,
\[P = \dfrac{1}{f}\]
Here, f denotes the focal length of the lens.
As we can observe that power and focal length of the lens have inverse relation in the context of each other. Therefore, the lens having the least magnitude of power will possess a higher magnitude of focal length. Hence, the lens having the power -3.5D will have the greater focal length.

Note:
To solve the above problem, it is necessary to remember the basic mathematical relation for the focal length and the power of the lens. These are inversely proportional to each other, such that changing one of these variables will cause the variation in another variable, at the desired value of the final conclusion.