A metal coin at the bottom of a beaker filled with a liquid of refractive index `4//3` to height of `6 cm`. To an observer looking from above the surface of the liquid, coin will appear at a depth of (consider paraxial rays).

Options

A. `7.5 cm`
B. `6.75 cm`
C. `4.5 cm`
D. `1.5 cm`

Explanation

To solve the problem of finding the apparent depth of a metal coin submerged in a liquid with a refractive index of \( \frac{4}{3} \), we can use the formula for apparent depth in optics. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a beaker filled with a liquid of height \( h = 6 \, \text{cm} \) and a refractive index \( \mu = \frac{4}{3} \). The observer is looking from above the surface of the liquid. We need to find the apparent depth \( h' \) of the coin.

### Step 2: Use the Formula for Apparent Depth
The formula for apparent depth when viewed from a medium of refractive index \( \mu \) is given by:
\[ h' = \frac{h}{\mu} \]
where:
- \( h' \) is the apparent depth,
- \( h \) is the real depth,
- \( \mu \) is the refractive index of the liquid.

### Step 3: Substitute the Values
Substituting the values into the formula:
- Real depth \( h = 6 \, \text{cm} \)
- Refractive index \( \mu = \frac{4}{3} \)

We get:
\[ h' = \frac{6 \, \text{cm}}{\frac{4}{3}} = 6 \, \text{cm} \times \frac{3}{4} \]

### Step 4: Calculate the Apparent Depth
Now, calculate \( h' \):
\[ h' = 6 \times \frac{3}{4} = \frac{18}{4} = 4.5 \, \text{cm} \]

### Conclusion
Thus, the coin will appear at a depth of \( 4.5 \, \text{cm} \).

### Final Answer
The apparent depth of the coin is \( 4.5 \, \text{cm} \).

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