Question

When Young's double slit experiment is performed in liquid, 8\(^\text{th}\) bright band is found to lie where 5\(^\text{th}\) dark band lies in air. Refractive index of liquid is

• A. 1.9
• B. 1.77
• C. 1.5
• D. 1.33

Hint:

In Young's double slit experiment, the refractive index of the medium affects the wavelength and the positions of the interference bands.

Answer 1

The Correct Option is B

Step 1: Understanding the shift in the band.
In Young's double slit experiment, the position of the bright and dark bands depends on the wavelength of the light and the refractive index of the medium. When the experiment is performed in a liquid, the wavelength of light in the liquid changes according to the refractive index \( n \), and the bands shift accordingly. Step 2: Relationship between bands.
The \( m \)-th dark band in air corresponds to the \( (m+3) \)-th bright band in the liquid. This shift occurs because the wavelength of light in the liquid decreases due to the refractive index. Therefore, the refractive index \( n \) is related to the shift by the equation: \[ n = \frac{8}{5} = 1.77 \] Step 3: Conclusion.
Thus, the refractive index of the liquid is \( 1.77 \), which corresponds to option (B).