Question

Given,\[1dioptre\] is equal to-
(A) $1m$
(B) $1cm$
(C) $1{m^{ - 1}}$
(D) $1c{m^{ - 1}}$

Answer 1

Hint: In order to answer this question, first we will choose the correct substitution for \[1 dioptre\] and then we will discuss the dioptre as it is the unit of one of the optics terms. And then we will also discuss the power of the human relaxed eye.

Complete answer:
Power has a unit of $D$ or dioptre which also relatable as:
$1D = 1{m^{ - 1}}$
A dioptre (British spelling) or diopter (American spelling) is a unit of measurement for a lens's optical power, which is equal to the reciprocal of the focal length in metres. As a result, it is a reciprocal length unit. A \[3 - dioptre\] lens, for example, focuses parallel rays of light at a distance of \[13{\text{ }}metres\] . The optical power of a flat window is zero dioptres, meaning it does not cause light to converge or diverge. Other reciprocals of distance, such as radii of curvature and the vergence of optical beams, are sometimes expressed in dioptres.
The fundamental advantage of utilising optical power instead of focal length is that the object distance, image distance, and focal length are all reciprocals in the lensmaker's equation. Another advantage is that when two or more comparably thin lenses are positioned close together, their powers roughly add up. As a result, a thin \[2.0 - dioptre\] lens combined with a thin \[0.5 - dioptre\] lens produces a focal length that is nearly identical to a single \[2.5 - dioptre\] lens.
Though the dioptre is based on the SI-metric system, it has not been included in the standard, so there is no international name or symbol for this unit of measurement—this unit for optical power would have to be specified explicitly as the inverse metre $({m^{ - 1}})$ within the international system of units. However, most languages have adopted the original term, and some national standardisation agencies, such as DIN, provide a unit name (dioptrie, dioptria, and so on) as well as the unit symbol dpt. The letter D is commonly used in the field of vision care.

Hence, the correct option is (C) $1{m^{ - 1}}$ .

Note:
The relaxed eye in humans has a total optical power of about \[60{\text{ }}dioptres\] . About two-thirds of this refractive power (about \[40{\text{ }}dioptres\] ) comes from the cornea, with the remaining one-third coming from the crystalline lens (about \[20{\text{ }}dioptres\] ). The ciliary muscle contracts during focusing to relieve the suspensory ligaments' strain or stress on the lens. This causes the lens to become more convex, which boosts the optical power of the eye. At age 15, the amplitude of accommodation is approximately \[11{\text{ }}to{\text{ }}16{\text{ }}dioptres\] , dropping to approximately 10 dioptres at age 25, and to approximately 1 dioptre at age 60.