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)
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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