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Question

# A lady uses +1.5 D glasses to have normal vision from 25 cm onwards. She uses a 20 D lens as a simple microscope to see an object. The maximum magnifying powers if she uses the microscope (a) together with the glasses and (b) without the glasses are

A
6, 6
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B
6, 9
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C
9, 6
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D
9, 9
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Solution

## The correct option is B 6, 9Convex lenses (with positive power) are used to correct hypermetropia (far-sightedness). Hence, we can estimate that the lady's near point is greater than the normal value (25 cm). Focal length of the correctional lens f=1P=11.5 D=10×10015 cm=2003 cm Power of the magnifier lens Pm=20 D Focal length of the magnifier fm=10020=5 cm Maximum magnification is given by m=1+Dfm Case (a) with correctional glasses The eye with correctional glasses will behave as a normal eye. Hence D=25 cm m=1+255=6 Case (b) without correctional glasses For an object at the normal near point (25 cm), the lens in the correctional glasses will form an image at her actual near point. Let the actual near point be v cm Then using lens formula, 1f=1v−1u u=D=25 cm, f=2003 cm ⇒v=−40 cm. So the actual near point is at 40 cm. Then magnification without correctional glasses m=1+40fo=1+405=1+8=9

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