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A biconvex lens has radii of curvature, 20 cm each. if the refractive index of the material of the lens is 1.5, the power of the lens is :
- a)+ 20 D
- b)+5D
- c)infinity
- d)+ 2 D
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A biconvex lens has radii of curvature, 20 cm each. if the refractive ...
R1 = R2 = 20 cm = 0.2 m
μ = 3/2
μ = 3/2
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A biconvex lens has radii of curvature, 20 cm each. if the refractive ...
To determine the power of a biconvex lens, we need to use the lens formula:
1/f = (n - 1) * (1/R1 - 1/R2)
where f is the focal length of the lens, n is the refractive index of the material, R1 is the radius of curvature of one side of the lens, and R2 is the radius of curvature of the other side of the lens.
Given that the radii of curvature of the lens are 20 cm each and the refractive index of the material is 1.5, we can substitute these values into the lens formula to find the power of the lens.
Substituting the values:
1/f = (1.5 - 1) * (1/20 - 1/20)
Simplifying the equation:
1/f = 0.5 * (0 - 0)
1/f = 0
Since the right side of the equation is zero, the left side must also be zero. This means that the focal length of the lens is infinity (f = ∞).
The power of a lens is given by the formula:
P = 1/f
Since the focal length is infinity, the power of the lens is also infinity. However, since infinity is not a practical value for power, we need to consider the limit of the power as the focal length approaches infinity.
As the focal length approaches infinity, the power of the lens approaches zero. This is because a lens with a very large focal length acts as a very weak lens and has a small power.
Therefore, the power of the biconvex lens in this case is approximately 0 D.
None of the given options (a), (b), (c), or (d) match the correct answer.
1/f = (n - 1) * (1/R1 - 1/R2)
where f is the focal length of the lens, n is the refractive index of the material, R1 is the radius of curvature of one side of the lens, and R2 is the radius of curvature of the other side of the lens.
Given that the radii of curvature of the lens are 20 cm each and the refractive index of the material is 1.5, we can substitute these values into the lens formula to find the power of the lens.
Substituting the values:
1/f = (1.5 - 1) * (1/20 - 1/20)
Simplifying the equation:
1/f = 0.5 * (0 - 0)
1/f = 0
Since the right side of the equation is zero, the left side must also be zero. This means that the focal length of the lens is infinity (f = ∞).
The power of a lens is given by the formula:
P = 1/f
Since the focal length is infinity, the power of the lens is also infinity. However, since infinity is not a practical value for power, we need to consider the limit of the power as the focal length approaches infinity.
As the focal length approaches infinity, the power of the lens approaches zero. This is because a lens with a very large focal length acts as a very weak lens and has a small power.
Therefore, the power of the biconvex lens in this case is approximately 0 D.
None of the given options (a), (b), (c), or (d) match the correct answer.
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A biconvex lens has radii of curvature, 20 cm each. if the refractive index of the material of the lens is 1.5, the power of the lens is :a)+ 20 D b)+5Dc)infinityd)+ 2 DCorrect answer is option 'B'. Can you explain this answer?
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