Final answer:
The index of the liquid is approximately 19.23.
Step-by-step explanation:
To find the index of the liquid, we can use the lens formula:
1/f = (n - 1)(1/R₁ - 1/R₂)
Where f is the focal length in meters, n is the refractive index of the lens, and R₁ and R₂ are the radii of curvature of the lens surfaces.
From the given information, we know that the focal length in air is 10 cm, so f = 0.10 m. We also know that the refractive index of the lens is 1.52. Plugging these values into the lens formula:
1/0.10 = (1.52 - 1)(1/∞ - 1/50)
Simplifying the equation gives:
10 = 0.52(0 - 1/50)
10 = -0.52/50
Solving for the refractive index of the liquid, we get:
1 - 10/0.52 = n - 1
n = 1 + 10/0.52
n ≈ 19.23
Therefore, the index of the liquid is approximately 19.23.