The concept required to solve this problem is the optical relationship that exists between the apparent depth and actual or actual depth. This is mathematically expressed under the equations.
[tex]d'w = d_w (\frac{n_{air}}{n_w})+d_g (\frac{n_{air}}{n_g})[/tex]
Where,
[tex]d_g =[/tex] Depth of glass
[tex]n_w =[/tex] Refraction index of water
[tex]n_g =[/tex] Refraction index of glass
[tex]n_{air} =[/tex] Refraction index of air
[tex]d_w =[/tex] Depth of water
I enclose a diagram for a better understanding of the problem, in this way we can determine that the apparent depth in the water of the logo would be subject to
[tex]d'w = d_w (\frac{n_{air}}{n_w})+d_g (\frac{n_{air}}{n_g})[/tex]
[tex]d'w = (1.7cm) (\frac{1}{1.33})+(4.2cm)(\frac{1}{1.52})[/tex]
[tex]d'w = 4.041cm[/tex]
Therefore the distance below the upper surface of the water that appears to be the logo is 4.041cm
