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 a refractive index

CONCEPT:

Lens Maker's Formula:

• If R1 and R2 are the radii of curvature of first and second refracting surfaces of a thin lens of focal length f and refractive index μ (w.r.t. surrounding medium) then the relation between f, μ, R1 and R2 are known as lens maker’s formula.
• The lens makers formula is given by 

\(\frac{1}{f} =\left ( \frac{μ _{1}}{μ _{2} } -1\right )\left ( \frac{1}{R_{1}}-\frac{1}{R_{2}} \right )\)

Where μ₁, μ₂ are refractive of the mediums

EXPLANATION:

Given - The biconvex lens of glass having refractive index 1.47

The equation of lens makers formula is given by 

\(\frac{1}{f} =\left ( \frac{μ _{l}}{μ _{c} } -1\right )\left ( \frac{1}{R_{1}}-\frac{1}{R_{2}} \right)\) ------------(1)

Where μ_l = refractive index of liquid and μ_c = refractive index  of the convex lens

• According to question, when a biconvex lens is dipped in a liquid, then it acts as a plane sheet of glass, therefore f = ∞ 

When a biconvex lens act as plane sheet then, it's focal length 

f = ∞

\(\Rightarrow \frac{1}{f} =0\)

Then equation 1 becomes 

\(\Rightarrow0 =\left ( \frac{μ _{l}}{μ _{c} } -1\right )\left ( \frac{1}{R_{1}}-\frac{1}{R_{2}} \right)\)

\(\Rightarrow 0 =\left ( \frac{μ _{l}}{μ _{c} } -1\right )\)

\(\Rightarrow {μ _{l}}={μ _{c} } \)

• The Refractive index of liquid  = Refractive index  of the convex lens