A plano-convex lens, when silvered on the plane side, behaves like a concave mirror of focal length 30 cm. When it is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of the material of the lens isa)2.0b)2.5c)1.5d)3.0Correct answer is option 'C'. Can you explain this answer?

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A plano-convex lens, when silvered on the plane side, behaves like a concave mirror of focal length 30 cm. When it is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of the material of the lens is

a)
2.0
b)
2.5
c)
1.5
d)
3.0

Correct answer is option 'C'. Can you explain this answer?

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A plano-convex lens, when silvered on the plane side, behaves like a c...

Given:
- A plano-convex lens behaves like a concave mirror of focal length 30 cm when silvered on the plane side.
- The same lens behaves like a concave mirror of focal length 10 cm when silvered on the convex side.

To Find:
The refractive index of the material of the lens.

Solution:

Let's analyze the two cases separately and then find the refractive index of the material.

Case 1: Lens silvered on the plane side
- When the plano-convex lens is silvered on the plane side, it behaves like a concave mirror of focal length 30 cm.
- The focal length of a concave mirror is given by the formula:

1/f = 2/R

where f is the focal length and R is the radius of curvature.

- In this case, the focal length is 30 cm, so

1/30 = 2/R

R = 60 cm

- The refractive index of the material of the lens can be calculated using the lens-maker's formula:

(μ - 1) * (1/R1 - 1/R2) = 1/f

where μ is the refractive index of the lens material, R1 is the radius of curvature of the convex side, R2 is the radius of curvature of the plane side, and f is the focal length.

- In this case, the lens is silvered on the plane side, so R2 is infinity. Therefore, the lens-maker's formula becomes:

(μ - 1) * (1/60 - 0) = 1/30

(μ - 1) * (1/60) = 1/30

(μ - 1) = 2

μ = 3

Case 2: Lens silvered on the convex side
- When the plano-convex lens is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm.
- Using the same formula as before:

1/f = 2/R

1/10 = 2/R

R = 20 cm

- Using the lens-maker's formula:

(μ - 1) * (1/R1 - 1/R2) = 1/f

- In this case, the lens is silvered on the convex side, so R1 is infinity. Therefore, the lens-maker's formula becomes:

(μ - 1) * (0 - 1/20) = 1/10

(μ - 1) * (-1/20) = 1/10

(μ - 1) = -2

μ = -1

However, since the refractive index cannot be negative, this solution is not valid.

Conclusion:
The refr

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A plano-convex lens, when silvered on the plane side, behaves like a c...

3. 1.5

Solution: Let the radius of curvature of the convex surface of the plano-convex lens be RRR. The focal length of a concave mirror is related to the radius of curvature by f=R2f = \frac{R}{2}f=2R.

When the plane side is silvered, the system behaves as a concave mirror with focal length 30 cm. The effective focal length fefff_{\text{eff}}feff of this system can be found using the mirror formula and lens formula combined, but given the scenario, we focus on this system.

When the convex side is silvered, the system behaves like a concave mirror with focal length 10 cm.

By using the relations for combined focal length and refractive index of the plano-convex lens, and applying these boundary conditions, the refractive index nnn of the material of the lens is determined to be 1.5.

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A plano-convex lens, when silvered on the plane side, behaves like a concave mirror of focal length 30 cm. When it is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of the material of the lens isa)2.0b)2.5c)1.5d)3.0Correct answer is option 'C'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A plano-convex lens, when silvered on the plane side, behaves like a concave mirror of focal length 30 cm. When it is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of the material of the lens isa)2.0b)2.5c)1.5d)3.0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plano-convex lens, when silvered on the plane side, behaves like a concave mirror of focal length 30 cm. When it is silvered on the convex side, it behaves like a concave mirror of focal length 10 cm. The refractive index of the material of the lens isa)2.0b)2.5c)1.5d)3.0Correct answer is option 'C'. Can you explain this answer?.

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