Question

In the Young's double slit experiment, when a glass plate of thickness 't' is introduced in the path of one of the slits, the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of glass plate is [refractive index of glass plate = 1.5, wavelength of light in vacuum is \(\lambda\)]

• A. \(2\lambda\)
• B. \(\frac{2\lambda }{3}\)
• C. \(\frac{\lambda }{3}\)
• D. \(\lambda\)

Hint:

A plate of thickness t adds an optical path (mu - 1)t; the intensity is unchanged when this equals a whole number of wavelengths.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
A glass plate of thickness \(t\) and refractive index \(\mu\) adds an extra optical path \((\mu-1)t\) to one beam.

Step 2: Condition
At the old central maximum the path difference was zero (bright). The intensity stays the same only if the new path difference is a whole number of wavelengths: \((\mu-1)t=m\lambda\).

Step 3: Calculation
For the minimum non-zero thickness take \(m=1\).
\((1.5-1)t=\lambda\Rightarrow 0.5\,t=\lambda\Rightarrow t=2\lambda\).

Final Answer:
The minimum thickness of the glass plate is \(2\lambda\). \[ \boxed{\text{(A) }2\lambda} \]