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NCERT Class XII Chapter
Ray Optics and Optical Instruments
Questions With Solutions

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Question : 26 of 38
Marks: +1, -0
A myopic person has been using spectacles of power – 1.0 dioptre for distant vision. During old age, he also needs to use separate reading glass of power + 2.0 dioptres. Explain what may have happened.
Solution:  
Myopic person uses spectacles of power – 1.0 dioptre or concave lens of focal length f = 1P\frac{1}{P} = - 100 cm in order to observe clearly object at infinity.
Far point of the person can be calculated as
1v1u\frac{1}{v} - \frac{1}{u} = 1f\frac{1}{f} or 1v1\frac{1}{v} - \frac{1}{-\infty} = 1100\frac{1}{-100} or v = - 100 cm
Similarly if the person uses spectacles of power + 2.0 dioptre then he must be using convex lens of power + 2.0 dioptre.
Focal length and near point can be calculated as
f = 1p\frac{1}{p} = 1+2\frac{1}{+2} = 0.5 m = 50 cm
For near point, 1v1u\frac{1}{v} - \frac{1}{u} = 1f\frac{1}{f}
1v125\frac{1}{v} - \frac{1}{-25} = 150\frac{1}{50} or 1v\frac{1}{v} = 150125\frac{1}{50} - \frac{1}{25}1v\frac{1}{v} = 1250\frac{1-2}{50} or v = - 50 cm
Thus the person also has the defect of hypermetropia and has a near point 50 cm. So having both defects he needs different lenses for distant vision and to see closer objects.
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