Question

If \( r \) and \( r' \) denote the angles inside the prism having angle of prism \( 50^\circ \), considering that during the interval of time from \( t = 0 \) to \( t = T \), \( r \) varies with time as \( r = 10^\circ + t^2 \). During this time \( r' \) will vary with time as 

• A. \( 50^\circ t^2 + t^2 \)
• B. \( 40^\circ t^2 - t^2 \)
• C. \( 40^\circ t^2 - t^2 \)
• D. \( 50^\circ t^2 - t^2 \)

Hint:

In problems involving the variation of angles inside a prism, the sum of the internal angles of the prism will always remain constant.

Answer 1

The Correct Option is D

For the given problem, we know the following information: - The angle of the prism is \( S_0 = 50^\circ \). - The angle \( r \) inside the prism varies with time as \( r = 10^\circ + t^2 \). Using Snell’s Law and the fact that the sum of the angles inside a prism equals the angle of the prism, we can relate the change in the angles \( r \) and \( r' \). The variation of \( r' \) is linked to \( r \), and since \( r = 10^\circ + t^2 \), we can use the relationship between these angles to determine the functional dependence of \( r' \) over time. Thus, \( r' \) will vary as \( r' = 50^\circ - t^2 \). Therefore, the correct answer is option (4): \( 50^\circ t^2 - t^2 \).