When a biconvex lens of glass having refractive index `1.47` is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index.

Options

A. equal to that of glass
B. less than one
C. greater than that of glass
D. less then that of glass

Answer

To solve the problem, we need to determine the refractive index of the liquid in which the biconvex lens is dipped, such that the lens behaves like a plane sheet of glass.

### Step-by-Step Solution:

1. **Understand the Condition**: The problem states that the biconvex lens acts as a plane sheet of glass when dipped in the liquid. This means that the light passing through the lens does not deviate, which occurs when the refractive index of the lens and the surrounding medium (the liquid) are equal.

2. **Identify the Refractive Index of the Lens**: The refractive index of the glass lens is given as \( n_g = 1.47 \).

3. **Set Up the Condition for No Deviation**: For the lens to act like a plane sheet, the refractive index of the liquid \( n_l \) must equal the refractive index of the lens. This is because when the refractive indices are the same, light rays will not bend as they enter or exit the medium.

4. **Equate the Refractive Indices**: Since the lens acts as a plane sheet, we can write:
\[ n_g = n_l \]
Substituting the known value:
\[ 1.47 = n_l \]

5. **Conclusion**: Thus, the refractive index of the liquid must be \( n_l = 1.47 \).

### Final Answer:
The refractive index of the liquid must be \( 1.47 \).

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