Snell's law for critical refraction at the boundary

Steps:

• The ray refracts along the plastic-air boundary at X, so the angle of refraction there is 90°.
• This makes the angle of incidence inside the plastic at X the critical angle θ_c = 49°, where n sin 49° = sin 90° = 1.
• For a rectangular block with parallel faces, the angle of incidence at X equals the angle of refraction r at the first air-plastic interface.
• Apply Snell's law at the first interface: sin I = n sin r = n sin 49°.

Why C is correct:

• It directly states Snell's law at the entry interface, with r = 49° matching the critical angle at X.

Why the others are wrong:

• A lacks the refractive index n and uses an invalid trigonometric relation sin I = sin 4I.
• B incorrectly sets r = 90° - I, which assumes a specific geometry not present.
• D uses sin 49I, an undefined angle (likely a typo for 49° but malformed).

Final answer: C