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A person suffering from myopia can see objects clearly only up to a distance of 50 cm. What should be the focal length and power of the corrective lens required?
50 cm, -2 D
+50 cm, +2 D
100 cm, -1 D
+100 cm, +1 D
50 cm, -2 D
To correct myopia (nearsightedness), a concave lens is used to shift the image of an object at infinity to the person's far point. Since the far point is 50 cm, the lens must create a virtual image of an object placed at infinity at this 50 cm mark.
To correct myopia (nearsightedness), a concave lens is used to shift the image of an object at infinity to the person's far point. Since the far point is 50 cm, the lens must create a virtual image of an object placed at infinity at this 50 cm mark.
Think of a concave lens as a 'diverging' bridge that allows your eyes to stop struggling and instead look at an object placed far away as if it were only 50 cm in front of you.
Mnemonic: 'Myopia needs Concave', just like 'My Con'.
f1тАЛ=v1тАЛтИТu1тАЛ тАФ Lens formula relating focal length, image distance, and object distance.
P=f┬а(in┬аcm)100тАЛ тАФ Power of a lens in Diopters (D) when focal length is in centimeters.
According to the lens formula, f1тАЛ=v1тАЛтИТu1тАЛ. For a person with myopia, u=тИЮ and v=тИТ50┬аcm (the far point). Substituting these values, f1тАЛ=тИТ501тАЛтИТтИЮ1тАЛ=тИТ501тАЛ. Thus, the focal length f=тИТ50┬аcm. The power P is calculated as P=f┬а(in┬аcm)100тАЛ=тИТ50100тАЛ=тИТ2┬аD.
Myopia (nearsightedness) occurs when the eyeball is too long or the lens is too curved.
A concave lens has a negative focal length and negative power.
The power of a lens is measured in Diopters (D), where 1┬аD=1┬аmтИТ1.
Concave lenses effectively move the far point from a finite distance back to infinity.
Corrective lenses only address the refractive error and do not 'cure' the physical elongation of the eyeball.
Spectacles for people who cannot read distant road signs.
Lenses in cameras to adjust focus for distant subjects.
The focal length is -50 cm because the lens is diverging.
Option B is incorrect because positive power (+2 D) belongs to a convex lens used for hypermetropia (farsightedness).
Options C and D reflect incorrect calculations of focal length and power.
A is correct тАФ The myopia correction requires a concave lens with a focal length of -50 cm, resulting in a power of -2 D.
Always remember: Myopia is distance-blind, needing negative power (concave), while Hypermetropia is near-blind, needing positive power (convex).
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