What Is Lateral Displacement in a Glass Slab? Causes, Formula, and Ray Diagram Explained
The Refraction of Light Through a Glass Slab is a classic JEE Main topic that explores how a light ray bends as it passes through a rectangular slab of glass. This phenomenon demonstrates the principles of ray optics and refraction in practical terms. Understanding this topic is vital for solving numerical problems, accurately drawing ray diagrams, and mastering optical laws relevant to examinations.
Introduction to Refraction of Light Through a Glass Slab
When a light ray travels from air (a rarer medium) into a glass slab (a denser medium), it changes direction—a process called refraction. The ray bends towards the normal inside the glass, and again as it exits, resulting in lateral displacement. Both the laws of refraction and geometrical considerations govern this behavior. The emergent ray remains parallel to the incident ray but shifted sideways.
Experimental Path and Double Refraction in Glass Slab
A typical experiment involves a glass slab placed on a sheet, with a light ray marked at an angle. The ray enters the slab at the air-glass interface, bends, then passes through the slab. As it exits at the glass-air interface, it bends again—this time away from the normal. This dual refraction causes the final ray to shift laterally, not just bend.
- Incident ray: enters the glass slab from air
- First refraction: at air-glass surface, ray bends towards normal
- Travel inside glass: straight path at reduced speed
- Second refraction: at glass-air surface, ray bends away from normal
- Emergent ray: parallel to the incident ray, but shifted sideways
This whole path obeys Snell’s law, which relates the angles and refractive indices of air and glass. Remember, two refractions always occur in a rectangular slab. The concept is different from refraction through a glass prism, where emergent rays deviate from the original line.
Key Laws and Formulae in Refraction of Light Through a Glass Slab
Snell’s law states: n1sin i = n2sin r. For a glass slab, n2 is the refractive index of glass, and n1 is that of air (often 1 in calculations). The angles i (angle of incidence) and r (angle of refraction) define the ray’s path.
A hallmark effect observed is the lateral displacement of the refracted ray. The formula used in JEE is:
| Parameter | Symbol | Unit |
|---|---|---|
| Lateral displacement | d | metre (m) |
| Thickness of slab | t | metre (m) |
| Angle of incidence | i | degree (°), radian (rad) |
| Angle of refraction | r | degree (°), radian (rad) |
| Refractive index (glass/air) | n | unitless |
The quantitative formula is:
d = t × sin(i - r) / cos(r), where:
- t = thickness of the glass slab
- i = angle of incidence
- r = angle of refraction
This setup is foundational for JEE Main, and is often tested along with derivations of lateral displacement and refractive index calculations.
Derivation and Worked Example: Lateral Displacement
The JEE Main syllabus expects a clear derivation of lateral displacement. Lateral displacement refers to the perpendicular distance between the direction of the incident ray and the emergent ray as they pass through the glass slab.
- The incident ray strikes the slab at angle i.
- It refracts at the first interface at angle r.
- Inside the slab, the ray travels a straight path of length t / cos r.
- At the second surface, the ray emerges at angle i (parallel to the incident ray).
- The perpendicular shift is found using geometry as d = t × sin(i - r) / cos r.
Example: If t = 1.0 cm, i = 45°, and n = 1.5 (glass to air), calculate r by Snell’s law, then substitute values. The emergent ray is found to be laterally shifted by about 0.37 cm.
You can use trigonometric identities and geometric reasoning for similar problems. Always state angles in degrees unless the question states otherwise.
Applications, Mistakes, and Exam Traps in Refraction of Light Through a Glass Slab
Understanding the Refraction of Light Through a Glass Slab has direct utility in optics, instrument design, and experimental physics. JEE Main frequently asks about mistakes in ray diagrams, sign conventions, and the difference from prism refraction.
- Ray diagrams: label normal, incidence, emergence, and displacement clearly
- Always account for both refractions in the slab
- Distinguish between slabs (no deviation, only shift) and prisms (true deviation)
- Remember slab displacement depends on angle of incidence
- Typical application: parallel glass windows, optical instrument panels
- Common trap: emergent ray is shifted, not angled; it's parallel to incident
Avoid mixing up the sign convention used in lenses and mirrors with slabs. Slabs shift light, prisms deviate.
Practice with mock tests and optics papers is recommended. Refer to concise revision notes for visual summaries of Snell’s law cases.
Vedantu provides expert-reviewed material, so checking topic notes and solved examples can boost your JEE exam performance. Always cross-check units and angle measures.
- If the slab is beveled or not rectangular, rays may not emerge parallel
- Add similar parallel examples using concepts from ray optics.
- Be precise with angle symbols and slab thickness in calculations
In summary, mastering the Refraction of Light Through a Glass Slab equips you for a variety of optics questions in JEE Main, strengthens your derivation skills, and deepens your grasp of wave and ray physics. Link each principle to previous optics fundamentals and practice regularly for clarity and speed.
FAQs on Refraction of Light Through a Glass Slab: Step-by-Step Explanation
1. What is refraction of light through a glass slab?
Refraction of light through a glass slab is the bending of a light ray as it passes from air into glass and then back into air, due to a change in speed at each boundary. The process involves:
- Light enters the glass slab and slows down, bending towards the normal.
- When exiting the slab, light speeds up and bends away from the normal.
- The emergent ray is parallel to the incident ray, but shifted sideways – this shift is called lateral displacement.
2. What is the formula for refraction of light through a glass slab?
The refraction formula for a glass slab is based on Snell's Law and lateral displacement. The main formulas are:
- Snell’s Law: n₁ sin i = n₂ sin r
- Lateral displacement (d): d = t × sin(i – r) / cos r where t is the thickness, i is the angle of incidence, and r is the angle of refraction.
3. How does light refract through a glass slab?
Light refracts through a glass slab by bending at both the entry and exit boundaries.
- At the air-glass interface, the light bends towards the normal due to slowing down.
- As it exits from glass to air, it bends away from the normal as it speeds up.
- The result is a parallel, laterally shifted emergent ray compared to the original incident ray.
4. What is lateral displacement in the context of a glass slab?
Lateral displacement is the sideways shift between the original incident ray and the emergent ray after passing through a glass slab.
- It occurs because of refraction at both parallel surfaces of the slab.
- The emergent ray remains parallel but is shifted due to the thickness of the slab and the angles involved.
- Lateral displacement depends on the slab’s thickness, the angle of incidence, and the refractive index of glass.
5. What are the laws of refraction through a glass slab?
The laws of refraction, also known as Snell’s laws, apply to a glass slab:
- The incident ray, the normal, and the refracted ray all lie in the same plane.
- The ratio of sine of the angle of incidence to the sine of the angle of refraction is constant, known as the refractive index: n = sin i / sin r.
- When the light exits, the emergent ray is parallel to the incident ray but laterally displaced.
6. How many refractions occur when light passes through a glass slab?
Two refractions occur as light travels through a glass slab:
- First, when light enters the glass from air (air to glass boundary).
- Second, when light exits the glass into air (glass to air boundary).
7. What is an activity to show the refraction of light through a glass slab?
To demonstrate refraction through a glass slab, you can perform this activity:
- Place a rectangular glass slab on a plain white sheet and draw its outline.
- Draw a straight line (incident ray) meeting one edge at an angle and mark the normal.
- Place pins along the incident ray, observe through the opposite side, and align more pins to obtain the emergent ray.
- Connect dots to trace the path of the light, observing the bending at both surfaces and the lateral displacement of the emergent ray.
8. What is the refractive index of a glass slab?
The refractive index of glass typically ranges from 1.5 to 1.6 for standard optical glass.
- It is calculated by the ratio: Refractive Index (n) = Speed of light in air / Speed of light in glass.
- The higher the refractive index, the more the light will bend when entering the glass.
9. What is the price of a glass slab used for refraction experiments?
The price of a glass slab for student experiments varies based on quality and size.
- Common laboratory glass slabs (rectangular, 10 cm × 5 cm × 1 cm) typically cost between ₹60 to ₹200 in India.
- Bulk quantity or high-precision models may be more expensive.
- They are widely available online and through educational science suppliers.
10. How is refraction through a glass prism different from a rectangular glass slab?
Refraction through a glass prism is different from a glass slab because the emergent ray is not parallel to the incident ray and dispersion can occur.
- In a glass slab, the emergent and incident rays are parallel but laterally displaced.
- In a prism, the emergent ray bends at an angle from the original path due to non-parallel sides and can split light into colors (dispersion).
11. Why does refraction of light through a glass slab occur?
Refraction through a glass slab occurs because light travels at different speeds in different media.
- When light passes from air (less optically dense) to glass (more optically dense), it slows down and bends towards the normal.
- On exiting glass to air, it speeds up and bends away from the normal.
- This change in speed and direction at each boundary results in lateral displacement.
12. What is shown in the diagram of refraction of light through a glass slab?
A diagram of refraction through a glass slab typically shows:
- An incident ray hitting the first surface at an angle.
- The refracted ray bending towards the normal inside the slab.
- The emergent ray bending away from the normal and appearing parallel to the incident ray but shifted sideways, showing lateral displacement.
