SATHEE: Ray Optics and Optical Instruments

Ray Optics and Optical Instruments - Result Question 41

42. The radius of curvature of a thin plano-convex lens is $10 c m$ (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) $10 c m$

(b) $15 c m$

(d) $5 c m$

[2000]

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Answer:

Correct Answer: 42. (a)

Solution:

(a) The silvered plano convex lens behaves as a concave mirro; whose focal length is given by $\frac{1}{F} = \frac{2}{f_{1}} + \frac{1}{f_{m}}$

If plane surface is silvered

$f_{m} = \frac{R_{2}}{2} = \frac{\infty}{2} = \infty$

$∴ \frac{1}{f_{1}} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$= (μ - 1) (\frac{1}{R} - \frac{1}{\infty}) = \frac{μ - 1}{R}$

$∴ \frac{1}{F} = \frac{2 (μ - 1)}{R} + \frac{1}{\infty} = \frac{2 (μ - 1)}{R}$

$F = \frac{R}{2 (μ - 1)}$

Here, $R = 10 c m, μ = 1.5$

$∴ F = \frac{10}{2 (1.5 - 1)} = 10 c m$

43 .

(b) $R_{1} = 60 c m, R_{2} = \infty, μ = 1.6$

$\frac{1}{f} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

$\frac{1}{f} = (1.6 - 1) (\frac{1}{60}) \Rightarrow f = 100 c m$ .

Ray Optics and Optical Instruments - Result Question 41

42. The radius of curvature of a thin plano-convex lens is $10 c m$ (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

Answer:

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Ray Optics and Optical Instruments - Result Question 41

42. The radius of curvature of a thin plano-convex lens is 10cm (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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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42. The radius of curvature of a thin plano-convex lens is $10 c m$ (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