Physics answers (i have a test tmrw and there is no key to this) thanks

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The discussion emphasizes the importance of following forum guidelines when seeking homework help, particularly for high school and undergraduate physics assignments. Users are required to post in the designated Homework & Coursework Questions area and must demonstrate an attempt to solve the problem before receiving assistance. The conversation highlights that graduate-level questions can be discussed in the main section if the student shows their work. Adhering to these rules ensures that the forum remains focused on educational discussions rather than direct academic assistance. Overall, participants are encouraged to show effort in their inquiries to foster a productive learning environment.
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https://www.physicsforums.com/showthread.php?t=414380

Show some effort.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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