To solve the problem step by step, we will follow the principles of optics and the properties of concave mirrors.
### Step 1: Determine the Focal Length of the Concave Mirror
The radius of curvature (R) of the concave mirror is given as 60 cm. The focal length (f) of a concave mirror is given by the formula:
\[
f = \frac{R}{2}
\]
Substituting the value of R:
\[
f = \frac{60 \, \text{cm}}{2} = 30 \, \text{cm}
\]
### Step 2: Identify the Position of the Image in Water
Since solar rays fall normally on the surface of the water, they will reflect off the mirror. The image formed by the concave mirror will be at the focal point, which is 30 cm above the mirror. However, we need to consider the height of the water.
The mirror is at the bottom of the tank, and the water level is 20 cm above the mirror. Therefore, the position of the image relative to the water surface is:
\[
\text{Distance of image from water surface} = \text{Height of water} - \text{Focal length}
\]
\[
= 20 \, \text{cm} - 30 \, \text{cm} = -10 \, \text{cm}
\]
This indicates that the image is actually formed 10 cm below the water surface.
### Step 3: Calculate the Apparent Shift Due to Refraction
Since the observer is in air and the image is formed in water, we need to account for the apparent shift due to the refractive index (μ) of water. The refractive index of water is given as \( \mu = \frac{4}{3} \).
The relation between real distance (d_real) and apparent distance (d_apparent) is given by:
\[
\frac{d_{\text{real}}}{d_{\text{apparent}}} = \mu
\]
Rearranging this gives:
\[
d_{\text{apparent}} = \frac{d_{\text{real}}}{\mu}
\]
Here, \( d_{\text{real}} = 10 \, \text{cm} \) (the distance below the water surface), so:
\[
d_{\text{apparent}} = \frac{10 \, \text{cm}}{\frac{4}{3}} = 10 \times \frac{3}{4} = 7.5 \, \text{cm}
\]
### Step 4: Determine the Final Position of the Image from the Water Surface
Since the apparent distance is 7.5 cm below the water surface, the distance of the image from the water surface is:
\[
\text{Distance of image from water surface} = 20 \, \text{cm} - 7.5 \, \text{cm} = 12.5 \, \text{cm}
\]
### Final Answer
Thus, the distance of the image from the surface of the water is:
\[
\text{Distance of the image from the surface of water} = 12.5 \, \text{cm}
\]
