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A person cannot see distinctly any object placed beyond 40cm from his eyes. Calculate the power of the lens which will help him to see distant objects clearly.
- a)+1 Dioptre
- b)-2.5 Dioptre
- c)-1.5 Dioptre
- d)+2 Dioptre
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A person cannot see distinctly any object placed beyond 40cm from his ...
A lens which can bring an object at infinity to 40 cm is required here.
So, u = infinity, v = -40 cm
We know, 1/f = 1/ v - 1/u
1/ f = 1/-40 - 1/infinity
So, f = -40 cm = -0. 4 m
Power of lens, P = 1/ f = 1/ -0. 4 = -2. 5 D
So, u = infinity, v = -40 cm
We know, 1/f = 1/ v - 1/u
1/ f = 1/-40 - 1/infinity
So, f = -40 cm = -0. 4 m
Power of lens, P = 1/ f = 1/ -0. 4 = -2. 5 D
Most Upvoted Answer
A person cannot see distinctly any object placed beyond 40cm from his ...
Given data:
Distance of the object = 40 cm
Distance of clear vision = infinity
We know that the formula for calculating the power of the lens is:
P = 1/f
where P is the power of the lens in dioptres and f is the focal length of the lens in meters.
Calculation:
As the person cannot see beyond 40 cm, we need to find the focal length of the lens that will help him see distant objects clearly.
Using the lens formula:
1/f = 1/v - 1/u
where v is the distance of clear vision (infinity) and u is the distance of the object (40 cm).
1/f = 1/infinity - 1/40 cm
1/f = 0 - 1/40 cm
1/f = -1/40 cm
f = -40 cm
The focal length of the lens is negative because the lens required is a concave lens (diverging lens) which has a negative focal length.
Now, using the formula P = 1/f, we get:
P = 1/-40 cm
P = -1/40 cm
P = -0.025 m^-1
P = -2.5 dioptres
Therefore, the power of the lens required to see distant objects clearly is -2.5 dioptres.
Distance of the object = 40 cm
Distance of clear vision = infinity
We know that the formula for calculating the power of the lens is:
P = 1/f
where P is the power of the lens in dioptres and f is the focal length of the lens in meters.
Calculation:
As the person cannot see beyond 40 cm, we need to find the focal length of the lens that will help him see distant objects clearly.
Using the lens formula:
1/f = 1/v - 1/u
where v is the distance of clear vision (infinity) and u is the distance of the object (40 cm).
1/f = 1/infinity - 1/40 cm
1/f = 0 - 1/40 cm
1/f = -1/40 cm
f = -40 cm
The focal length of the lens is negative because the lens required is a concave lens (diverging lens) which has a negative focal length.
Now, using the formula P = 1/f, we get:
P = 1/-40 cm
P = -1/40 cm
P = -0.025 m^-1
P = -2.5 dioptres
Therefore, the power of the lens required to see distant objects clearly is -2.5 dioptres.
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A person cannot see distinctly any object placed beyond 40cm from his ...
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A person cannot see distinctly any object placed beyond 40cm from his eyes. Calculate the power of the lens which will help him to see distant objects clearly.a)+1 Dioptreb)-2.5 Dioptrec)-1.5 Dioptred)+2 DioptreCorrect answer is option 'B'. Can you explain this answer?
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