Nearsightedness and Farsightedness, (rays and lenses)

Part A:

The lens should form the image at the far point.

-3.5m

Part C:

The lens should form the image at the near point.

Part D:

(1/0.6) + (1/-0.350) = -1.19

-1.19^-1 = -0.84

Part AWhen glasses (or contact lenses) are used to correctnearsightedness,the corrective lens should form the image at thefar point.The far point of the nearsighted eye is not infinity andmay be less than 1 m.The maximum focal length of the nearsightedeye is insufficient to produce a sharp image on theretina,and raysfrom a distant object converge to a focus in front of theretina.Part BThe nearsighted person has a far point that is d_f =3.50 m from the eye.The focal length f₁ of the contactlenses that the personwould need to see an object at infinityclearly is(1/d_f) + (1/D) = (1/f)Here,D = 25 cm = 0.25 mor (1/f) = (1/3.50) + (1/0.25) = (10/35) + (100/25) = (50 +700/175) = (750/175)or f = (175/750) = 0.233 cm = 0.233 * 10^-2mPart CWhen glasses (or contact lenses) are used to correctfarsightedness,the corrective lens should form should form theimage at the near point.A farsightedperson can usually see farobjects clearly but not nearby objects.Although the near point of anormal eye is approximately 25 cm,the near point of afarsightedperson is much farther away.The refracting power in the cornea andlens is insufficient to focus the light from all but distantobjectssatisfactorily.Part DThe near point of the farsighted person is d₁=0.600 mThe book is held at d₂= 0.350 m from the person'seye.The focal length of the contact lenses is(1/f₂) = (1/d₁) +(1/d₂)or (1/f₂) = (1/0.600) + (1/0.350)or (1/f₂) = (100/60) + (100/35) = (700 + 1200/420)= (1900/420)or f₂ = (420/1900) = 0.221 m.