Question:
Young's double slit experiment is conducted with monochromatic light of wavelength \(5000\,\text{\AA}\), with slit separation of \(3\,\text{mm}\) and observer at \(20\,\text{cm}\) away from the slits. If a \(1\,\text{mm}\) transparent plate is placed in front of one of the slits, the fringes shift by \(6\,\text{mm}\). The refractive index of the transparent plate is
Young's double slit experiment is conducted with monochromatic light of wavelength \(5000\,\text{\AA}\), with slit separation of \(3\,\text{mm}\) and observer at \(20\,\text{cm}\) away from the slits. If a \(1\,\text{mm}\) transparent plate is placed in front of one of the slits, the fringes shift by \(6\,\text{mm}\). The refractive index of the transparent plate is
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In YDSE, the fringe shift due to a thin transparent plate is
\[
S=\frac{D}{d}(\mu-1)t
\]
where \(t\) is the thickness of the plate.
Updated On: Jun 22, 2026
- \(1.08\)
- \(1.09\)
- \(1.1\)
- \(1.2\)
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The Correct Option is B
Solution and Explanation
Step 1: Use fringe shift formula due to a transparent plate.
When a transparent plate of thickness \(t\) and refractive index \(\mu\) is placed in front of one slit, fringe shift is given by \[ S=\frac{D}{d}(\mu-1)t \] where \[ S=6\,\text{mm} \] \[ D=20\,\text{cm}=200\,\text{mm} \] \[ d=3\,\text{mm} \] and \[ t=1\,\text{mm} \]
Step 2: Substitute the values.
\[ 6=\frac{200}{3}(\mu-1)(1) \] \[ \mu-1=\frac{6\times 3}{200} \] \[ \mu-1=\frac{18}{200} \] \[ \mu-1=0.09 \]
Step 3: Find refractive index.
\[ \mu=1+0.09 \] \[ \mu=1.09 \]
Step 4: Final conclusion.
Therefore, the refractive index of the transparent plate is \[ \boxed{1.09} \]
When a transparent plate of thickness \(t\) and refractive index \(\mu\) is placed in front of one slit, fringe shift is given by \[ S=\frac{D}{d}(\mu-1)t \] where \[ S=6\,\text{mm} \] \[ D=20\,\text{cm}=200\,\text{mm} \] \[ d=3\,\text{mm} \] and \[ t=1\,\text{mm} \]
Step 2: Substitute the values.
\[ 6=\frac{200}{3}(\mu-1)(1) \] \[ \mu-1=\frac{6\times 3}{200} \] \[ \mu-1=\frac{18}{200} \] \[ \mu-1=0.09 \]
Step 3: Find refractive index.
\[ \mu=1+0.09 \] \[ \mu=1.09 \]
Step 4: Final conclusion.
Therefore, the refractive index of the transparent plate is \[ \boxed{1.09} \]
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