Through a glass slab
Show on a big screenA ray goes into a glass block and comes out. Is it still on the same line?
- A ray meets a glass slab at angle i to the normal.
- Going in, it bends towards the normal.
- Going out, it bends away. It leaves parallel to the first ray.
- The leaving ray is shifted sideways. That gap is d.
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Slide the angle and the thickness. Watch the shift.
The rule
Usually not. It comes out on a new line, shifted sideways. A slab is a flat block of glass with two parallel faces.
A glass slab has air on both sides. A ray leaves it parallel to the ray that entered. It is shifted sideways. The shift is the lateral displacement. It is the gap between the two rays. Measure it at right angles to them.
The two faces are parallel. The bend at the second face undoes the bend at the first. So the direction is the same.
The shift is zero along the normal. It grows with thicker glass. It grows with a bigger angle of incidence. It grows with a higher refractive index. Along the normal, the ray does not bend. It comes out on the same line.
Worked example
A slab is 6 cm thick, with n = 1.5. A ray enters at i = 45°.
Here t is the thickness of the slab. The shift is d.
In the glass, the ray's path has length t / cos r. The shift is that path times sin(i − r).
sin r = sin 45° / 1.5 = 0.471, so r = 28.1°.
Then i − r = 45° − 28.1° = 16.9°.
d = t sin(i − r) / cos r = 6 × sin 16.9° / cos 28.1° = 6 × 0.290 / 0.882 = 2.0 cm
Try the lab to finish this lesson.