A plane mirror is fixed at the bottom of a tank containing water. A small object is kept at a height of 24 cm from the bottom and is viewed from a point vertically above it. The distance between the object and the image in the mirror as appears to the person is

Options

A. 48 cm
B. 64 cm
C. 36 cm
D. 54 cm

Answer

To solve the problem step by step, we need to follow these instructions:

### Step 1: Understand the setup
We have a plane mirror fixed at the bottom of a tank filled with water. An object is placed at a height of 24 cm from the bottom of the tank. We need to find the distance between the object and its image as seen from a point directly above the object.

**Hint:** Visualize the scenario with a diagram to understand the position of the object and the mirror.

### Step 2: Identify the height of the object
The height of the object from the bottom of the tank is given as 24 cm.

**Hint:** Remember that the height is measured from the bottom of the tank to the object.

### Step 3: Determine the position of the image
In a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it. Therefore, if the object is 24 cm above the bottom of the tank, the image will also appear to be 24 cm below the mirror.

**Hint:** Use the property of plane mirrors that states the distance of the image from the mirror is equal to the distance of the object from the mirror.

### Step 4: Calculate the total distance between the object and the image
The total distance between the object and the image can be calculated as follows:
- The distance from the object to the mirror is 24 cm.
- The distance from the mirror to the image is also 24 cm.

Thus, the total distance (D) between the object and the image is:
\[ D = \text{Distance from object to mirror} + \text{Distance from mirror to image} = 24 \, \text{cm} + 24 \, \text{cm} = 48 \, \text{cm} \]

**Hint:** Add the distances from the object to the mirror and from the mirror to the image to find the total distance.

### Step 5: Consider the effect of the medium
Since the object is viewed through water, we need to consider the refractive index of water. The effective distance as perceived by the observer is given by the formula:
\[ \text{Effective Distance} = \frac{D}{\mu} \]
where \( D \) is the distance calculated and \( \mu \) is the refractive index of water (1.33).

Substituting the values:
\[ \text{Effective Distance} = \frac{48 \, \text{cm}}{1.33} \approx 36 \, \text{cm} \]

**Hint:** Remember to divide the total distance by the refractive index to account for the medium through which the image is viewed.

### Conclusion
The distance between the object and the image as it appears to the person is approximately 36 cm.

**Final Answer:** 36 cm