Physics · Ch 6 — Optics
Refraction in Glass Slab
Refraction in Glass Slab
When a ray of light passes through a parallel-sided glass slab of thickness and refractive index , it refracts twice: entering the slab (rarer air to denser glass) it bends towards the normal, and leaving the slab (denser glass back to rarer air) it bends away from the normal by exactly the same amount, so the emergent ray ends up travelling exactly parallel to the original incident ray, only shifted sideways by a perpendicular distance called the lateral displacement (or lateral shift). Drawing a perpendicular from the exit point to the (extended) undeviated original path and working through the resulting right-triangle geometry ( and ) gives . This shows the …
What this figure shows. A ray enters a parallel-sided glass slab of thickness t at incidence angle i, bending towards the normal to refraction angle r as it crosses into the glass, then bending back away from the normal by the same angle r as it leaves the far side, so the emergent ray is exactly parallel to the original incident ray. A perpendicular CE is dropped from the exit point to the extended original (undeviated) path, marking the lateral displacement L; using the two right triangles this perpendicular …
Worked out. A glass slab of thickness 0.25 m and refractive index 1.5 is struck by a ray at incidence angle i = 60 degrees. Applying Snell's law, sin r = sin(60 degrees)/1.5 = 0.577, giving r = 35.25 degrees. Substituting into L = t sin(i-r)/cos r gives L = 0.25 times sin(60 - 35.25) divided by cos(35.25 degrees) = 0.25 times sin(24.75 degrees)/cos(35.25 degrees), which works out to L = 0.1281 m, i.e. the lateral displacement is 12.81 cm -- a sizeable sideways shift for a fairly thick slab struck at a fairly steep angle, consistent with the rule that thicker slabs and larger incidence angles both increase the la …