Question

As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water (μ = 4/3). The height of water is the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ____cm.

Answer 1

Correct Answer: 98

Step 1: Apparent Depth of \( O \) 

The relationship between apparent depth and real depth in a medium is given by:

\[ \text{Apparent depth} = \frac{\text{Real depth}}{\mu}, \]

where:

• \(\text{Real depth (d)} = 8 \, \text{cm}\),
• \(\mu = \frac{4}{3}\) (refractive index of the medium).

Substitute the values:

\[ \text{Apparent depth of } O = \frac{8}{\frac{4}{3}} = 6 \, \text{cm}. \]

Step 2: Distance Between \( O \) and \( I_2 \)

1. Total real depth of the liquid column:
2. Refracted depth (Apparent shift):
3. Distance between \( O \) and \( I_2 \):

Final Answer:

• Apparent depth of \( O \): \( 6 \, \text{cm} \)
• Distance between \( O \) and \( I_2 \): \( 98 \, \text{cm} \)