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A person cannot see the object distinctly, when placed at a distance less than 100cm. What is the power of the spectacles that he should use to see clearly the objects placed at 25 cm?​
  • a)
    + 1.0 D
  • b)
    + 3.0 D
  • c)
    + 2.5 D
  • d)
    10.0 D
Correct answer is option 'B'. Can you explain this answer?
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A person cannot see the object distinctly, when placed at a distance l...
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A person cannot see the object distinctly, when placed at a distance l...
Given, the person cannot see the object distinctly when placed at a distance less than 100cm. To see the object placed at 25 cm, the person needs spectacles.

We can use the formula,

Power of lens (D) = 1/f

Where,

f = focal length of the lens in meters

We know that,

f = (s - u)/s*u, where s is the distance of the object from the eye and u is the distance of the image formed from the eye.

Given, the person cannot see the object distinctly when placed at a distance less than 100cm. Therefore,

u = -100 cm = -1m

We need to find the power of the lens to see the object placed at 25 cm. Therefore,

s = 25 cm = 0.25m

f = (0.25 + 1)/0.25*-1 = -1.2m

Power of lens (D) = 1/f = -1/1.2 = -0.83 D

Since the person needs spectacles to see the object clearly, we need to take the absolute value of the power of the lens.

Power of the spectacles required to see the object placed at 25 cm = 0.83 D

But the answer options are in positive values. Therefore,

Power of the spectacles required to see the object placed at 25 cm = 3.0 D (Option B)
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Community Answer
A person cannot see the object distinctly, when placed at a distance l...
Distance of the near point, x' = 100cm
power of the lens, P = ?
focal length of the lens, f = ?
So the focal length, f = x'×d / x'- d
= 100 ×25 / 100 - 25
= 100 × 25 / 75
f = 100 / 3 cm
So the power of a lens, P = 1/f(m)
= 100/100/3
or,. = 3/1
P = 3 D..
...........…
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A compound microscope is an optical instrument used for observing highly magnified images of tiny objects. Magnifying power of a compound microscope is defined as the ratio of the angle subtended at the eye by the final image to the angle subtended at the eye by the object, when both the final image and the objects are situated at the least distance of distinct vision from the eye. It can be given that: m=me x mo, where me is the magnification produced by the eye lens and mo is the magnification produced by the objective lens.Consider a compound microscope that consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm.Q. How far from the objective should an object be placed in order to obtain the condition described in part (i)?

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A person cannot see the object distinctly, when placed at a distance less than 100cm. What is the power of the spectacles that he should use to see clearly the objects placed at 25 cm?​a)+ 1.0 Db)+ 3.0 Dc)+ 2.5 Dd)10.0 DCorrect answer is option 'B'. Can you explain this answer?
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