91Ó°ÊÓ

We need to find out :

a) Whether we can see the marks from the top of the tank going down, or from the bottom of the tank coming up.

b) The lowest or highest mark that can be seen.

The ray coming from the top mark of the tank is incident on the top surface at a very high angle which will lead to Total internal reflection and the ray will never reach the eyes of the person.

But the ray from the mark near the bottom of the tank will incident at a small angle and hence the ray will refract and will reach the eyes of the person as shown below.

Critical angle is expressed as :

$$\begin{gathered} {\mathrm{θ}}_c={\sin }^{-1}\left(\frac{n_2}{n_1}\right) \\ {\mathrm{θ}}_c={\sin }^{-1}\left(\frac{1.00}{1.33}\right) \\ {\mathrm{θ}}_c=48.75° \end{gathered}$$

Highest mark seen corresponds to the light ray reaching to the top surface at critical angle.

Therefore for the figure,

$$\begin{gathered} \tan {\mathrm{θ}}_c=\frac{65cm}{x} \\ x=\frac{65cm}{\tan (48.75)°} \\ x=57cm. \end{gathered}$$

So the highest mark that can be seen is 60 cm.