What is Lateral Displacement?

S6-SA3-0154

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Lateral displacement is the perpendicular distance between the original path of a light ray and its final path when it emerges from a transparent material, like a glass slab. It tells us how much the light ray shifts sideways after passing through the material.

Simple Example

Quick Example

Imagine you are watching a cricket match on TV. If you place a thick glass paperweight on top of a player's name on the screen, the name seems to shift slightly sideways when you look through the glass. This sideways shift is similar to lateral displacement.

Worked Example

Step-by-Step

Let's calculate the lateral displacement of a light ray passing through a glass slab.

Step 1: Given values - Angle of incidence (i) = 60 degrees, Refractive index of glass (n) = 1.5, Thickness of slab (t) = 5 cm.

Step 2: Use Snell's Law to find the angle of refraction (r): n1 * sin(i) = n2 * sin(r). Here, n1 (air) = 1. So, 1 * sin(60) = 1.5 * sin(r).

Step 3: sin(r) = sin(60) / 1.5 = 0.866 / 1.5 = 0.577.

Step 4: r = arcsin(0.577) approx 35.26 degrees.

Step 5: Use the formula for lateral displacement (d): d = t * sin(i - r) / cos(r).

Step 6: d = 5 * sin(60 - 35.26) / cos(35.26) = 5 * sin(24.74) / cos(35.26).

Step 7: d = 5 * 0.418 / 0.816 approx 2.56 cm.

Answer: The lateral displacement is approximately 2.56 cm.

Why It Matters

Understanding lateral displacement is crucial in designing optical instruments like telescopes and microscopes, used by scientists and engineers. It helps in creating clear images in cameras and even in medical imaging devices, opening doors to careers in optics and medical technology.

Common Mistakes

MISTAKE: Confusing lateral displacement with angular deviation (how much the light ray bends). | CORRECTION: Lateral displacement is a *distance* (sideways shift), while angular deviation is an *angle* (change in direction). They are related but distinct.

MISTAKE: Assuming lateral displacement only depends on the angle of incidence. | CORRECTION: It also depends on the thickness of the material and its refractive index. A thicker slab or higher refractive index generally leads to greater displacement.

MISTAKE: Using the angle of incidence directly in the displacement formula without finding the angle of refraction. | CORRECTION: The formula for lateral displacement involves both the angle of incidence (i) and the angle of refraction (r), so 'r' must be calculated first using Snell's Law.

Practice Questions

Try It Yourself

QUESTION: A light ray enters a glass slab (refractive index = 1.6) at an angle of incidence of 45 degrees. If the angle of refraction is 26.2 degrees, and the slab thickness is 4 cm, what is the approximate lateral displacement? | ANSWER: 1.57 cm

QUESTION: If a light ray passes through two identical glass slabs placed one after another, will the total lateral displacement be double that of a single slab? Explain why. | ANSWER: Yes, if the slabs are perfectly aligned and the light ray enters the second slab parallel to its path after the first. The displacement from each slab adds up.

QUESTION: A light ray strikes a glass slab of thickness 't' at an angle of incidence 'i'. If the refractive index of the glass is 'n', derive the formula for lateral displacement in terms of t, i, and r (angle of refraction). | ANSWER: d = t * sin(i - r) / cos(r)

MCQ

Quick Quiz

Which of the following factors does NOT directly influence the lateral displacement of a light ray passing through a glass slab?

Thickness of the glass slab

Refractive index of the glass slab

Colour (wavelength) of the light ray

Intensity (brightness) of the light ray

The Correct Answer Is:

Lateral displacement depends on the angle of incidence, refractive index, thickness of the slab, and the wavelength (colour) of light. The intensity or brightness of light does not affect how much it shifts sideways.

Real World Connection

In the Real World

Lateral displacement is used in fibre optics, which powers our internet and mobile data. When light signals travel through optical fibres, the slight displacement ensures the signal stays within the core, allowing fast data transfer for things like UPI transactions or watching live cricket matches on your phone.

Key Vocabulary

Key Terms

INCIDENCE: The striking of a light ray on a surface | REFRACTION: The bending of light as it passes from one medium to another | REFRACTIVE INDEX: A measure of how much a medium bends light | THICKNESS: The extent of a material between its two surfaces

What's Next

What to Learn Next

Next, explore 'Dispersion of Light through a Prism'. You'll see how different colours of light have slightly different refractive indices, leading to varying lateral displacements, which causes white light to split into a rainbow!