A concave mirror of radius of curvature 60 cm is placed at the bottom of tank containing water upto a height of 20 cm. The mirror faces upwards with its axis vertical. Solar light falls normally on the surface of water and the image of the sun is formed. If `""_(a)mu_(w)=4/3` then with the observer in air, the distance of the image from the surface of water is:

Options

A. 30 cm
B. 10 cm
C. 7.5 cm above
D. 7.5 cm below

Answer

To solve the problem step by step, we will follow the principles of optics, particularly focusing on the behavior of concave mirrors and the effect of a medium (water) on the light rays.

### Step-by-Step Solution:

1. **Identify the Radius of Curvature and Focal Length**:
- 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:
\[ f = \frac{R}{2} \]
- Therefore,
\[ f = \frac{60 \, \text{cm}}{2} = 30 \, \text{cm} \]

**Hint**: Remember that for concave mirrors, the focal length is negative, but since we are dealing with distances, we will use the absolute value for calculations.

2. **Determine the Real Depth**:
- The depth of water in the tank is 20 cm. The distance from the mirror to the surface of the water is the focal length minus the height of the water:
\[ \text{Real Depth} = f - \text{Height of Water} = 30 \, \text{cm} - 20 \, \text{cm} = 10 \, \text{cm} \]

**Hint**: The real depth is the distance from the mirror to the water surface, which is the focal length minus the height of the water.

3. **Calculate the Appropriate Depth**:
- The refractive index of water (\(\mu_w\)) is given as \( \frac{4}{3} \).
- The appropriate depth (d) can be calculated using the formula:
\[ \text{Appropriate Depth} = \frac{\text{Real Depth}}{\mu_w} \]
- Substituting the values:
\[ d = \frac{10 \, \text{cm}}{\frac{4}{3}} = 10 \, \text{cm} \times \frac{3}{4} = 7.5 \, \text{cm} \]

**Hint**: The appropriate depth accounts for the effect of the medium (water) on the light rays, which causes them to appear closer to the surface than they actually are.

4. **Determine the Distance of the Image from the Surface of Water**:
- The distance of the image from the surface of the water is equal to the appropriate depth calculated above. Thus, the image of the sun is formed at a distance of:
\[ \text{Distance of Image from Water Surface} = 7.5 \, \text{cm} \]

**Hint**: The image distance is measured from the surface of the water to the point where the light rays converge after reflecting off the mirror.

### Final Answer:
The distance of the image from the surface of the water is **7.5 cm**.