Question

An air bubble in a glass slab with a refractive index of $1.5$ (near-normal incidence) is $5cm$ deep when viewed from one surface and $3cm$ deep when viewed from the opposite face. What is the thickness (in cm) of the slab?

Answer 1

Step 1: Given

Refractive index: $\mu =1.5$

Apparent depth from one side: $D_1\text{'}=5cm$

Apparent depth from another side: $D_2\text{'}=3cm$

Step 2: Formula Used

$D\text{'}=\frac{D}{\mu }$Where $D\text{'}$is the apparent depth, $D$ is the real depth and $\mu$ is the refractive index.

Step 3: Find the real depths

Calculate the real depth from the first side by using the formula.

$$\begin{gathered} D_1\text{'}=\frac{D_1}{\mu } \\ \Rightarrow 5cm=\frac{D_1}{1.5} \\ \Rightarrow D_1=5cm\times 1.5 \\ \Rightarrow D_1=7.5cm \end{gathered}$$

Calculate the real depth from another side by using the formula.

$$\begin{gathered} D_2\text{'}=\frac{D_2}{\mu } \\ \Rightarrow 3cm=\frac{D_2}{1.5} \\ \Rightarrow D_2=3cm\times 1.5 \\ \Rightarrow D2=4.5cm \end{gathered}$$

Step 3: Find the thickness of the slab

Calculate the thickness of the slab by adding both the real depths.

$$\begin{gathered} Thickness=D_1+D_2 \\ =7.5cm+4.5cm \\ =12cm \end{gathered}$$

The thickness (in cm) of the slab is $12cm$.