Question

The apparent depth of an air bubble in a glass slab of refractive index $1.5$ is $5cm$ when viewed from one face and $2cm$ when viewed from opposite face. The thickness of glass slab is

• A. 10 cm
• B. 10.5 cm
• C. 7 cm
• D. 7.5 cm

Answer 1

The correct option is B 10.5 cm

$\mathrm{Apparent}\mathrm{depth}\left(h\right)=\frac{\mathrm{real}\mathrm{depth}\left(H\right)}{\mathrm{refractive}\mathrm{index}\mathrm{of}\mathrm{second}\mathrm{medium}\left(n_{21}\right)}$
Apparent depth from one side$\left(h_1\right)=5\mathrm{cm}$
Apparent depth from other side $\left(h_2\right)=2\mathrm{cm}$
Now,
Real depth from one side$\left(H_1\right)=h_{1}x{n}_{21}=5x1.5=7.5\mathrm{cm}$Real depth from other side
$\left(H_2\right)=h_{2}x{n}_{21}=2x1.5=3\mathrm{cm}$Therefore, thickness of glass slab = $H_1+H_2=7.5+3=10.5\mathrm{cm}$