Before You Begin
Question #43050
The Question
In a Fresnel's biprism experiment performed in air, a monochromatic point source of light of wavelength is placed at a distance from a biprism. The biprism has a refractive index and a small refracting angle . The interference fringes are observed on a screen placed at a distance from the source. The observed fringe width is . The entire apparatus is now completely immersed in a transparent liquid of refractive index . Assuming the small angle approximation holds, what is the new fringe width observed on the screen?
Options
- A.
0.90 \text{ mm}
- B.
0.225 \text{ mm}
- C.
1.20 \text{ mm}
- D.
0.40 \text{ mm}
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Variable_Constraint
Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.
Concepts Behind This Question
Fringe Width Invariance|Young's Double Slit Geometry|Microscope Tube Length
Why This Question Is Tricky
Common Mistakes
This question tests the synthesis of wave optics and ray optics by exploiting the apparent shift of virtual sources in a refractive medium.
A common trap is assuming the virtual source separation 'd' is a fixed geometric constant, leading students to only scale the wavelength () and incorrectly obtain .
Conversely, students might recalculate the deviation angle using the relative refractive index but forget to scale the wavelength, yielding .
The correct approach requires modifying both the optical path difference geometry and the wavelength, which elegantly cancels the liquid's refractive index from the final algebraic expression.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Wave Optics - Class 12 |
| Concept | Fringe Width Invariance |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |