How Does Lateral Displacement of Light Occur in a Glass Slab?
Lateral displacement of light describes the sideways shift of a light ray as it passes obliquely through a parallel-sided glass slab and emerges parallel to its original direction, but offset by a certain distance. This effect is a classic application of refraction, deeply rooted in Snell’s law, and is frequently tested in JEE Main Physics under ray optics. Understanding the underlying principle, formula derivation, and visual ray diagrams is essential for tackling related problems and for building conceptual accuracy in optics.
Definition and Visualisation of Lateral Displacement of Light
When a light ray enters a transparent rectangular glass slab at an angle, it refracts towards the normal upon entry and away as it exits, causing the emergent ray to remain parallel but laterally shifted. The lateral displacement of light is the perpendicular distance between the original incident ray’s path and its emergent counterpart. You’ll encounter terms like lateral shift of light, glass slab lateral displacement, and “lateral displacement of light ray” for this concept.
- The ray emerges parallel to but displaced from the incident ray.
- A normal ray (perpendicular to the surface) exhibits zero lateral displacement.
- Both “lateral shift of ray through glass” and “lateral displacement of light through glass slab” point to the same JEE syllabus concept.
- The amount of displacement increases with slab thickness and angle of incidence.
- Lateral displacement only occurs for oblique incidence, not for normal rays.
Visualising this effect with a ray diagram builds clarity. The incident ray strikes at an angle, refracts in the slab, and finally emerges parallel but shifted—a must-draw for many JEE Main optics questions.
Derivation and Formula for Lateral Displacement of Light
The quantitative value of lateral displacement of light, typically denoted by d, can be derived using refraction through a glass slab and simple geometry.
- Consider a slab of thickness t, refractive index μ, with incident angle i and refraction angle r.
- Using Snell’s law: μ = sin i / sin r.
- The emergent ray is parallel to the incident ray but shifted sideways.
- The formula is: d = t × (sin(i - r) / cos r).
- t = thickness of the glass slab (m)
- i = angle of incidence (degrees or radians)
- r = angle of refraction (degrees or radians)
- d = lateral displacement of light (m)
| Symbol | Quantity | SI Unit |
|---|---|---|
| d | Lateral displacement | metre (m) |
| t | Thickness of slab | metre (m) |
| i | Angle of incidence | radian / degree |
| r | Angle of refraction | radian / degree |
| μ | Refractive index | dimensionless |
This derivation is a standard exercise in ray optics. Remember, the small angle approximation is sometimes accepted for JEE questions, simplifying sin θ ≈ θ and cos θ ≈ 1 for very small angles.
Factors Affecting Lateral Displacement of Light
- Thickness t: As slab thickness increases, lateral displacement increases.
- Angle of incidence i: Greater angles produce more lateral shift, up to a critical value.
- Refractive index μ: Denser materials (higher μ) cause greater displacement.
- Wavelength: Slightly affects refractive index, so color matters minutely.
- No displacement if incident angle is zero (light falls normally).
You should connect this analysis to the experiment measuring lateral shift through glass—a common practical.
Lateral Displacement of Light Versus Refraction and Diffraction
It is crucial to contrast lateral displacement with refraction and diffraction to avoid classic MCQ pitfalls. Lateral displacement is a result of sequential refraction at parallel surfaces. Refraction involves bending of light at a single interface. Diffraction involves spreading of light around edges. Only the first produces a parallel, shifted emergent ray.
| Aspect | Lateral Displacement | Refraction | Diffraction |
|---|---|---|---|
| Emergent ray | Parallel, shifted sideways | Bent at boundary | Spread, not shifted parallel |
| Medium shape | Parallel-sided slab | Any interface | Edge/aperture involved |
| JEE focus | Numericals, diagrams | Basic law, Snell’s law | Interference, fringes |
Reviewing such contrasts prepares you for tricky MCQs that test conceptual nuances rather than rote formulas.
- Do not confuse lateral displacement of light with simply “change of direction” (that’s refraction).
- “Lateral shift of light” always implies a parallel emergent ray, distinct from deviation in prisms.
- Errors often involve missing the dependence on angle or slab thickness.
Worked Example: Calculating Lateral Displacement of Light
A ray of light strikes a glass slab (thickness t = 2.0 cm, μ = 1.5) at i = 45°, finds r via Snell’s law first:
- μ = sin i / sin r ⇒ 1.5 = sin 45° / sin r ⇒ sin r = sin 45° / 1.5 ≈ 0.4714 ⇒ r ≈ 28°
- d = t × sin(i – r) / cos r
- sin(i – r) = sin(17°) ≈ 0.292
- cos r ≈ 0.882
- d = 2.0 × 0.292 / 0.882 ≈ 0.66 cm
In exam situations, always state the formula, substitute values with correct units, and box the final result.
- As seen in optics revision notes, remembering units and symbol definitions is key to scoring full marks.
- Practising with optics mock tests and diagrams cements the method.
Applications, Pitfalls, and Quick Recall
- Instrument error analysis when aligning light beams.
- Design of shift-compensating lenses and windows.
- Laboratory determination of refractive index uses measured displacement.
- Exam trap: forgetting that for normal incidence, lateral displacement is zero.
- Apply for JEE Main workflow: Always draw the thick slab diagram with accurate normals and angles.
The lateral displacement of light concept is foundational for advanced optics topics appearing in JEE Main. Mastery of its formula and conditions benefits allied topics like glass slab refraction, prism deviation, and comparison with reflection and refraction phenomena.
- For reinforcement, consult the Vedantu optics revision notes.
- Test your conceptual sharpness with the optics mock test.
- Expand to related pages, e.g., prism and difference between reflection and refraction, for complete exam coverage.
Content here is curated by experts with JEE Main coaching experience and strictly tracks the exam syllabus. Vedantu ensures accuracy by cross-verifying formulae and common exam variants, bridging understanding from theory to problem-solving for every JEE aspirant.
FAQs on Lateral Displacement of Light Explained for JEE & Boards
1. What is lateral displacement of light?
Lateral displacement of light refers to the sideways shift a light ray experiences as it passes obliquely through a parallel-sided glass slab, emerging parallel but shifted from its original path.
Key features include:
- The incident and emergent rays are parallel but not collinear.
- The shift depends on thickness, angle of incidence, and refractive index.
- It is a core concept in ray optics and important for JEE and board exams.
2. How does lateral displacement happen?
Lateral displacement happens when a light ray enters a glass slab at an angle, gets refracted twice, and emerges parallel but shifted sideways.
- At each interface, refraction of light occurs according to Snell's Law.
- The path inside the slab is oblique due to the change in medium.
- The ray emerges parallel to its original direction but displaced horizontally — this is called the lateral shift.
3. What is the formula for lateral displacement?
The formula for lateral displacement (d) is:
d = t · sin(i - r) / cos(r)
Where:
- t = thickness of the slab
- i = angle of incidence
- r = angle of refraction
4. What factors affect the lateral displacement of light?
The lateral displacement increases or decreases depending on several factors:
- Thickness (t) of the glass slab: Greater thickness = more displacement.
- Angle of incidence (i): Larger angle = greater displacement.
- Refractive index (μ): Higher refractive index = greater bending and displacement.
- Wavelength of light: Different colors (wavelengths) may shift differently due to dispersion.
5. What is the difference between lateral displacement and refraction?
Refraction is the bending of light when it passes between media of different refractive index, while lateral displacement is the sideways shift resulting from refraction in a parallel-sided slab.
- Refraction involves change in direction at the interface.
- Lateral displacement refers to the net shift after passing through the slab.
6. What happens if the light ray falls normally on the glass slab?
When a light ray falls normally (at 90°) on a glass slab, lateral displacement is zero because there is no change in direction (angle of incidence i = 0), and the emergent ray follows the same straight-line path.
- No deviation or shift occurs.
- Lateral displacement = 0.
7. Can lateral displacement occur in curved or non-parallel slabs?
Lateral displacement, as defined in standard optics, specifically occurs in parallel-sided slabs.
- In curved or non-parallel slabs, light undergoes deviation but not uniform lateral displacement.
- The emergent ray's path may not remain parallel to the incident ray.
8. Does the color or wavelength of light affect lateral displacement?
Yes, the color/wavelength of light can affect lateral displacement because the refractive index of glass varies slightly with wavelength.
- Shorter wavelengths (like blue) refract more and can show slightly greater lateral displacement than red light.
- This principle is also seen in dispersion.
9. Why is the emergent ray parallel but not coincident with the incident ray?
The emergent ray is parallel but not coincident because the light is refracted twice inside the slab—towards the normal when entering and away from the normal when exiting.
- This results in the ray coming out parallel (due to equal prism angles) but shifted sideways — this shift is called lateral displacement.
10. How can lateral displacement be measured experimentally?
Lateral displacement can be measured using a simple glass slab experiment in school labs:
- Draw an incident ray at an angle on paper and mark the outline of a rectangular glass slab.
- Trace the emergent ray and remove the slab.
- Draw perpendiculars to measure the distance between incident and emergent rays; this is the lateral displacement.
11. What is lateral displacement of light Class 10?
In Class 10 Physics, lateral displacement is defined as the sideways shift between the original path of a light ray and the path it takes after passing obliquely through a glass slab.
- The emergent ray is parallel but shifted.
- It forms the basis for understanding practical ray optics, experiment setups, and exam questions.
12. What are the applications of lateral displacement in daily life or optics?
Lateral displacement is used in several optical instruments and practical applications:
- In glass lenses and optical instruments to correct image alignment.
- In scientific experiments to understand beam alignment.
- It is an essential concept for understanding refraction, prisms, and optical path corrections.
