When a biconvex lens of glass having refractive index 1.5 is dipped in a liquid, it acts like a plane glass slab. This implies that liquid has refractive index 

When a biconvex lens of glass having refractive index 1.5 is dipped in a liquid, it behaves as if it were a plane sheet of glass. This observation can help us determine the refractive index of the liquid. Here's how:

Step-by-Step Explanation

1. Understanding the Problem: When a biconvex lens of glass having refractive index 1.5 is immersed in a liquid, the lens no longer functions as a lens but as a plane sheet. This indicates that its focal length becomes infinite.

2. Using the Lensmaker's Formula: The focal length of a lens is described by the lensmaker's formula:

                   1/f = (μg - μL) (1/R1 - 1/R2)
   

   Here:

   • μ_g = Refractive index of the glass (1.5).
   • μ_L = Refractive index of the liquid.
   • R₁ and R₂ = Radii of curvature of the lens surfaces.

3. Setting the Focal Length to Infinity: Since the lens behaves like a plane sheet, its focal length becomes infinite. Therefore:

                   1/f = 0
   

4. Rewriting the Equation: Substituting into the lensmaker's formula:

                   0 = (μg - μL) (1/R1 - 1/R2)

   This equation will hold true if:

                   μg - μL = 0
   

   Or:

                   1/R1 - 1/R2 = 0
   

5. Analyzing the Conditions: When a biconvex lens of glass having refractive index is used, the radii of curvature (R₁ and R₂) are different and typically have opposite signs. Therefore, the term (1/R₁ - 1/R₂) cannot be zero.

6. Equating the Refractive Indices: To satisfy the equation, we conclude:

                   μg = μL
   

   Hence, the refractive index of the liquid equals that of the glass.

7. Final Calculation: Given that the refractive index of the glass is 1.5, the refractive index of the liquid must also be:

                   μL = 1.5