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?

Open in App
Solution

## Step 1: GivenRefractive 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 depthsCalculate the real depth from the first side by using the formula.${D}_{1}\text{'}=\frac{{D}_{1}}{\mu }\phantom{\rule{0ex}{0ex}}⇒5cm=\frac{{D}_{1}}{1.5}\phantom{\rule{0ex}{0ex}}⇒{D}_{1}=5cm×1.5\phantom{\rule{0ex}{0ex}}⇒{D}_{1}=7.5cm$Calculate the real depth from another side by using the formula.${D}_{2}\text{'}=\frac{{D}_{2}}{\mu }\phantom{\rule{0ex}{0ex}}⇒3cm=\frac{{D}_{2}}{1.5}\phantom{\rule{0ex}{0ex}}⇒{D}_{2}=3cm×1.5\phantom{\rule{0ex}{0ex}}⇒D2=4.5cm$Step 3: Find the thickness of the slabCalculate the thickness of the slab by adding both the real depths.$Thickness={D}_{1}+{D}_{2}\phantom{\rule{0ex}{0ex}}=7.5cm+4.5cm\phantom{\rule{0ex}{0ex}}=12cm$The thickness (in cm) of the slab is $12cm$.

Suggest Corrections
0
Explore more