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The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm?
Most Upvoted Answer
The radius of curvature of a thin plano-convex lens is 10 cm (of curve...
1/f= (1.5-1)[1/10-1/infinity] = 1/20
means, f = 20
after silvering effective focal length become half so, it will be f/2
We get, f(effective) = 20/2 = 10cm
means, f = 20
after silvering effective focal length become half so, it will be f/2
We get, f(effective) = 20/2 = 10cm
Community Answer
The radius of curvature of a thin plano-convex lens is 10 cm (of curve...
Introduction:
When a plano-convex lens is silvered on the plane surface, it behaves like a concave mirror. In this case, the focal length of the resulting mirror can be determined based on the radius of curvature of the lens and the refractive index of the material.
Given data:
- Radius of curvature of the lens (R) = 10 cm
- Refractive index of the lens material (n) = 1.5
Deriving the focal length:
The formula to calculate the focal length (f) of a lens is given by:
1/f = (n - 1) * (1/R1 - 1/R2)
In this case, since the lens is plano-convex, one of the radii of curvature (R1) is infinite. Therefore, the formula simplifies to:
1/f = (n - 1) / R
Substituting the given values, we get:
1/f = (1.5 - 1) / 10
1/f = 0.5 / 10
f = 10 / 0.5
f = 20 cm
Conclusion:
The focal length of the silvered plano-convex lens, when it behaves like a concave mirror, is 20 cm. Therefore, the correct option is (c) 20 cm.
Note:
- The radius of curvature of the curved surface of the lens is given. This is because the curved surface is the one which contributes to the lens action, while the plane surface acts as a mirror.
- The refractive index of the lens material is used in the calculation because it affects the bending of light rays passing through the lens.
When a plano-convex lens is silvered on the plane surface, it behaves like a concave mirror. In this case, the focal length of the resulting mirror can be determined based on the radius of curvature of the lens and the refractive index of the material.
Given data:
- Radius of curvature of the lens (R) = 10 cm
- Refractive index of the lens material (n) = 1.5
Deriving the focal length:
The formula to calculate the focal length (f) of a lens is given by:
1/f = (n - 1) * (1/R1 - 1/R2)
In this case, since the lens is plano-convex, one of the radii of curvature (R1) is infinite. Therefore, the formula simplifies to:
1/f = (n - 1) / R
Substituting the given values, we get:
1/f = (1.5 - 1) / 10
1/f = 0.5 / 10
f = 10 / 0.5
f = 20 cm
Conclusion:
The focal length of the silvered plano-convex lens, when it behaves like a concave mirror, is 20 cm. Therefore, the correct option is (c) 20 cm.
Note:
- The radius of curvature of the curved surface of the lens is given. This is because the curved surface is the one which contributes to the lens action, while the plane surface acts as a mirror.
- The refractive index of the lens material is used in the calculation because it affects the bending of light rays passing through the lens.
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The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm?
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The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm?.
The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of curvature of a thin plano-convex lens is 10 cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length(a) 10 cm(b) 15 cm(c) 20 cm(d) 5 cm?.
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