Glass Slab Refraction and Lateral Shift: A Clear Picture

A glass slab is a thick piece of glass with parallel faces, like a window pane or a rectangular block. Light passing through it bends at both surfaces but emerges parallel to its original direction, shifted sideways. This shift explains many simple observations.

The effect is important for understanding apparent depth, microscope slide observations, and optical instruments. Even though the ray direction does not change overall, the sideways displacement can be measured precisely.

Key Concepts

Glass slab: Transparent block thickness t in metres or centimetres, refractive index n about 1.5 for crown glass.

Lateral shift d: Perpendicular distance between original incident ray extended and emergent ray. Measured in same unit as t.

Normal shift: Apparent depth change when viewed normally. Real depth divided by n gives apparent depth.

• Incident and emergent rays are parallel
• Shift increases with thickness and angle of incidence
• At normal incidence shift is zero

Formulas

Snell law at each surface: sin i divided by sin r = n for air to glass, and reverse at second surface. n dimensionless, angles in degrees.

Lateral shift d = t times sin(i minus r) divided by cos r. Here t is slab thickness, i incidence angle, r refraction angle inside glass. Assumes slab in air with parallel faces.

Apparent depth = real depth divided by n. For object under slab viewed normally. This is normal shift = real depth times (1 minus 1 divided by n).

Worked Example

A glass slab thickness 6 cm, n = 1.5, ray incident at 45 degrees. Find refraction angle and lateral shift.

1. Snell: sin r = sin i divided by n = sin 45 degrees divided by 1.5 = 0.707 divided by 1.5 = 0.471, so r = 28.1 degrees.
2. Compute i minus r = 45 minus 28.1 = 16.9 degrees, sin = 0.291, cos r = cos 28.1 = 0.882.
3. d = t sin(i minus r) divided by cos r = 6 times 0.291 divided by 0.882 = 1.98 cm.

Emergent ray is parallel to incident ray but shifted about 2.0 cm sideways. If viewed normally, an object under slab appears raised by 6 times (1 minus 1 divided by 1.5) = 2 cm.

Common Misconceptions

• Emergent ray bends again outward direction changes: For parallel slab, emergent ray is parallel to incident. Net deviation zero, only shift.
• Lateral shift depends only on thickness: It also depends strongly on i and n. At normal incidence shift zero regardless of thickness.
• Apparent depth is same as lateral shift: Apparent depth is vertical shift for normal viewing. Lateral shift is sideways for oblique viewing.

Real-World Applications

• Microscope focusing must account for apparent raising of specimen through glass slide
• Window glass shifts images slightly, noticeable at oblique view in thick glass
• Optical instruments use slabs for beam displacement without changing direction
• Measuring refractive index by real and apparent depth using travelling microscope

A glass slab refracts twice, emerging ray parallel but laterally shifted by d = t sin(i minus r) divided by cos r. This simple result neatly explains apparent depth and displacement experiments.