Explain the path of a light ray through a right-angled isosceles prism when the critical angle is 42 degrees…

Question

Explain the path of a light ray through a right-angled isosceles prism when the critical angle is 42 degrees and the incident ray enters perpendicular to one face.

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Here are the solutions to the questions:

1)

The ray enters the prism perpendicularly to the first face.
When a ray enters a medium perpendicularly, it passes undeviated.
The ray then travels to the hypotenuse face.
Since it's a right-angled isosceles prism, the angles are $90^\circ$ , $45^\circ$ , and $45^\circ$ . The angle of incidence at the hypotenuse face is $45^\circ$ (measured from the normal).
Compare the angle of incidence with the critical angle.
The critical angle is given as $42^\circ$ . Since the angle of incidence ( $45^\circ$ ) is greater than the critical angle ( $42^\circ$ ), Total Internal Reflection (TIR) occurs.
The ray reflects off the hypotenuse face.
The angle of reflection is equal to the angle of incidence, so the ray reflects at $45^\circ$ .
After reflection, the ray strikes the second shorter face perpendicularly.
It then exits the prism undeviated.
\begin{tikzpicture}[scale=1.5] % Prism vertices \coordinate (A) at (0,2); \coordinate (B) at (0,0); \coordinate (C) at (2,0); % Draw prism \draw (A) -- (B) -- (C) -- cycle; % Incident ray \draw[->, thick] (-1,1.5) -- (0,1.5); % Incident ray \draw[dashed] (0,1.5) -- (0,0.5); % Normal at first surface (not needed as ray is perpendicular) % Ray inside prism (first segment) \draw[thick] (0,1.5) -- (1.5,0); % Ray travels to hypotenuse % Normal at hypotenuse \draw[dashed] (1.5,0) -- (1.5,1.5); % Normal at hypotenuse \node at (1.6, 0.75) {$N$}; % Angles at hypotenuse \pic [draw, angle radius=5mm, "45$^\circ$"] {angle = {1.5,1.5}--(1.5,0)--(0,1.5)}; % Angle of incidence \pic [draw, angle radius=5mm, "45$^\circ$"] {angle = {1.5,1.5}--(1.5,0)--(3,0)}; % Angle of reflection (relative to normal) % Reflected ray inside prism \draw[thick] (1.5,0) -- (3,0); % Reflected ray to second short face % Exit ray \draw[->, thick] (3,0) -- (4,0); % Exit ray (perpendicular to face) % Right angle symbol \draw (0.2,0.2) rectangle (0,0); \draw (1.8,0.2) rectangle (2,0); % Right angle at C \draw (0.2,1.8) rectangle (0,2); % Right angle at A \draw (1.8,0.2) rectangle (2,0); % Right angle at C % Angles of prism \pic [draw, angle radius=5mm, "45$^\circ$"] {angle = {0,0}--(2,0)--(0,2)}; \pic [draw, angle radius=5mm, "45$^\circ$"] {angle = {2,0}--(0,2)--(0,0)}; \end{tikzpicture}
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4)
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Explain the path of a light ray through a right-angled isosceles prism when the critical angle is 42 degrees and the incident ray enters perpendicular to one face.

Step-by-step solution

The ray enters the prism perpendicularly to the first face.

The ray then travels to the hypotenuse face.

Compare the angle of incidence with the critical angle.

The ray reflects off the hypotenuse face.

After reflection, the ray strikes the second shorter face perpendicularly.

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