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Question #43890
The Question
A plano-convex lens of radius of curvature and refractive index is placed with its convex surface facing a point source . The plane surface of the lens is perfectly silvered. The point source is placed on the principal axis at a distance from the convex surface. It emits monochromatic light of wavelength . The reflected light forms an interference pattern localized at the convex surface of the lens. Assuming the central thickness of the lens is such that the exact center of the interference pattern is a bright fringe, what is the radius of the first dark ring?
Options
- A.
- B.
- C.
- D.
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Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Multi-Concept_Bridge
Master problems that require linking physics and math concepts to solve complex competitive questions.
Concepts Behind This Question
Lens Silvering Logic|Optical Instrument Magnification|Coherence Requirement
Why This Question Is Tricky
Common Mistakes
This question tests the synthesis of geometrical optics (lens silvering) and wave optics (interference).
The 'Lethal Collision' occurs when students treat the silvered lens purely as a single equivalent mirror, calculating only the final image location () and completely ignoring the partial reflection at the first dielectric interface.
By failing to recognize that the front surface acts as a secondary coherent virtual source, they miss the interference phenomenon entirely.
The problem forces the student to independently track both the front-surface reflection and the transmitted-reflected-transmitted wave, calculate their respective virtual source locations, and apply the phase-coherence conditions for a spherical and plane wave superposition.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Ray Optics and Optical Instruments - Class 12 |
| Concept | Lens Silvering Logic |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |