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Put a glass block on a line drawn on paper and look through its edge. The line seems broken, as if part of it has slid sideways. That is lateral shift: light leaves a parallel-sided slab in its original direction, but displaced. This post derives the formula, works two problems with numbers, and shows when a quick approximation is safe.
What do NCERT and CBSE say?
The NCERT Class 10 chapter Light – Reflection and Refraction traces a ray through a rectangular slab in Activity 9.10 and notes that the emergent ray is parallel to the incident ray but "shifted sideward slightly". The NCERT Class 12 chapter Ray Optics and Optical Instruments says a ray through a rectangular slab has no deviation "but it does suffer lateral displacement/shift" (Fig. 9.9). The CBSE Physics curriculum for 2026-27 lists an activity "to observe refraction and lateral deviation of a beam of light incident obliquely on a glass slab", and the JEE (Main) 2026 syllabus includes refraction at plane surfaces. Check your exam year's syllabus.
Why does the ray come out parallel?
At the first face, light bends towards the normal: sin i = n sin r. At the second face, parallel to the first, it meets the normal at r and bends back out to i. The two bends are equal and opposite, so there is no change of direction. The only effect is a sideways step.
How do you derive the formula?
Let the slab have thickness t. Inside the glass the ray makes angle r with the normal, so the path length inside is t / cos r. The original direction makes angle i with the normal, so the path inside the glass is turned by (i − r) from where the ray would have gone. The perpendicular distance between the two parallel lines is the path length times sin(i − r):
d = t sin(i − r) / cos r
Two limits make sense of it. At normal incidence, i = r = 0 and d = 0. At grazing incidence, as i approaches 90°, d approaches t.
Worked example 1: a neat angle
A slab 6.0 cm thick has n = √3. Light strikes it at 60°. Find the lateral shift.
sin r = sin 60° / √3 = (√3/2) / √3 = 1/2, so r = 30°.
d = 6.0 × sin(60° − 30°) / cos 30° = 6.0 × 0.5 / 0.866 ≈ 3.46 cm, which is exactly 2√3 cm.
The light travels 6.0 / cos 30° ≈ 6.93 cm inside the glass.
Worked example 2: a calculator angle
A slab 5.0 cm thick has n = 1.5. Light strikes it at 45°.
sin r = 0.7071 / 1.5 ≈ 0.471, so r ≈ 28.1°.
i − r ≈ 16.9°, and sin 16.9° ≈ 0.290. Also cos 28.1° ≈ 0.882.
d ≈ 5.0 × 0.290 / 0.882 ≈ 1.65 cm.
When can you use a small-angle shortcut?
For small i, sin(i − r) ≈ i − r, cos r ≈ 1 and r ≈ i/n, which gives
d ≈ t i (1 − 1/n), with i in radians.
For n = 1.5, the shortcut is within about 1% of the exact value at i = 10°, but about 20% too low at 45°. Use it for estimates and small angles only, and use the exact formula in an exam unless the question asks for an approximation.
Which mistakes cost marks?
Mixing up lateral and normal shift. Our post on apparent depth and normal shift covers the other one.
Using degrees in the small-angle formula. Convert i to radians.
Measuring d along the slab face. The shift is the perpendicular distance between the two parallel rays.
Expecting a deviation. For parallel faces, the direction does not change.
Writing sin r = n sin i. Going from air into glass, sin i = n sin r. The history of that law is in our profile of Willebrord Snell.
A practice routine
Day 1: Derive d = t sin(i − r)/cos r from a sketch, without notes.
Day 2: Make a table of d/t for i = 15°, 30°, 45°, 60° and 75° with n = 1.5, and watch it rise towards 1.
Day 3: Do the slab activity with four pins and a glass block, then compare your measured shift with the formula.
Day 4: Solve two problems that ask for n given d, t and i.
Day 5: Test yourself on a mixed set of refraction problems. Dunlosky and colleagues (2013) rated practice testing and spaced practice as the most useful study techniques.
If you want to see how the shift changes with angle, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Tonight, calculate the lateral shift for i = 30° through a 5.0 cm slab with n = 1.5, then check it against your table from Day 2.
