Light

 The reason we write

$$9=\frac{6}{1.5}+\frac{8}{{\mu }_B}$$

comes directly from how apparent depth works when light passes through multiple transparent layers.

Let me break it down clearly.

⭐ Core Concept: Apparent depth in multiple media

When you look at an object (like a coin) through several transparent layers, each layer makes the object appear closer than it really is.

Each layer contributes its own “apparent depth,” given by:

$$\text{Apparent depth of layer}=\frac{\text{Real depth}}{\text{Refractive index}}$$

So if there are two liquids, A and B:

• Liquid A contributes: $\frac{d_A}{{\mu }_A}$

• Liquid B contributes: $\frac{d_B}{{\mu }_B}$

The total apparent depth is the sum of these two contributions:

$$\text{Total apparent depth}=\frac{d_A}{{\mu }_A}+\frac{d_B}{{\mu }_B}$$

⭐ Apply to your problem

Liquid A:

• Depth = 6 cm

• Refractive index = 1.5

Liquid B:

• Depth = 8 cm

• Refractive index = ${\mu }_B$

Total apparent depth of coin = 9 cm

So:

$$9=\frac{6}{1.5}+\frac{8}{{\mu }_B}$$

This equation simply says:

The coin appears 9 cm deep because the “apparent depth effect” of liquid A plus the “apparent depth effect” of liquid B adds up to 9 cm.

⭐ Why do we add them?

Because light bends twice:

1. Once when passing through liquid A

2. Again when passing through liquid B

Each bending makes the coin appear higher (closer), and the total shift is the sum of both effects.

If you want, I can also explain apparent depth or refraction in multiple layers in more detail.