Mary\'s old prescription corrected her vision when her near pointwas at 60cm, bu

Question

Mary's old prescription corrected her vision when her near pointwas at 60cm, but her eyesight is getting worse. Now she needs newglasses with a power of 2.67 Diopters. Assume n=2.
1. What's the power of her old glasses? 2. Where is her new near point located? 3. Is she getting more nearsighted/farsighted? EXPLAIN! 4. If you're trying to modify her old glasses to correct hervision, do you need to make the lenses flatter or more curved?EXPLAIN! 5. What is the fractional change (1 -rnew/rold) in the radius of curvature of thesymmetric thin lenses that will achieve the desired result?
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1. What's the power of her old glasses? 2. Where is her new near point located? 3. Is she getting more nearsighted/farsighted? EXPLAIN! 4. If you're trying to modify her old glasses to correct hervision, do you need to make the lenses flatter or more curved?EXPLAIN! 5. What is the fractional change (1 -rnew/rold) in the radius of curvature of thesymmetric thin lenses that will achieve the desired result?
Please show ALL work! I promise to rate you as lifesaver ifyour answer is correct!

Explanation / Answer

taking actual near point as object distance and changed nearest point of accomodation as imagedistance        1 /f = 1 /p + 1/ q       1 /f = 1/25.0cm + 1 / -60cm since the image is virtual taking negative for qvalue from the above relation we can solve for f     f = 43 cms positive values of f indicates , converging lense (1)power of old lense p = 1/ f (2) given the new focal length f ' = 100 /2.67 =37.5cm        and new nearest point 'q' ' can be determined as          1/ p + 1 /q'= 1 /f'      p = 25cms from the abv relation we can solve for q' >60cm (3) the curvature of the lense must be decreased so as todecrease the focal length,     she is getting more farsightedness , sincethe capabilitys to see near by obejects is increasing . 4) we need to flatter than the previous . 5) focal length and radius are related as f = -R/2      we know fnew,foldare 43 cms and 37.5cm using (1 - rnew/rold) =(1- fold/fnew )         

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