A laser beam of wavelength 650 nm passes through a flat glass slab of thickness 3 cm and refractive index 1.5. The lateral displacement of the emergent beam is measured to be 0.25 cm. Calculate the angle of incidence (to the normal) of the laser beam on the slab.

Step-by-step solution

1. Let the angle of incidence be θi and the refracted angle be θt.
2. Use Snell’s law: $sin{\theta }_t=\frac{sin{\theta }_i}{n}=\frac{sin{\theta }_i}{1.5}$.
3. Express the lateral shift: $d=t,sin({\theta }_i-{\theta }_t)$, where $t=3$ cm and $d=0.25$ cm.
4. Set up the equation: $0.25=3,sin({\theta }_i-{\theta }_t)$.
5. Iteratively solve for θi; a reasonable estimate is θi≈14° (plugging 14° gives $d\approx 0.25$ cm).
6. Thus the incident angle is approximately 14°.

Concept tested: Lateral shift in a glass slab

Published 4 October 2026 · How this solution was prepared and checked