How Does Light Refract Through a Glass Slab?

Refraction of light through a glass slab is a fundamental concept in ray optics, involving the change in direction and speed of light as it passes from one medium to another. This phenomenon is governed by the principles of geometrical optics and is significant for various applications and examinations such as JEE Main.

Overview of Refraction through a Glass Slab

When a ray of light enters a glass slab from air, its speed decreases due to the higher optical density of glass. This causes the ray to bend towards the normal at the point of incidence. As the ray exits into air, it bends away from the normal, resulting in the emergent ray being parallel but laterally displaced from the incident ray.

The process involves two stages of refraction — first at the air-glass interface and then at the glass-air interface. Both interfaces must be considered for accurate analysis. For detailed topics related to refraction, refer to Refraction Of Light Through A Glass Slab.

Explanation of the Path of Light in a Glass Slab

The incident ray first strikes the glass slab at an angle, known as the angle of incidence. Upon entering the denser glass, it refracts towards the normal due to reduced velocity. Inside the slab, the ray travels in a straight line, maintaining a constant angle with the normal, which is the angle of refraction.

On emerging from the opposite face of the slab, the ray moves from the denser glass to the rarer air, bending away from the normal. The emergent ray remains parallel to the incident ray, but is shifted sideways. This shift is known as lateral displacement.

This phenomenon is distinct from deviation in prisms, where the emergent ray is not parallel to the incident ray. Additional details on prism refraction can be found in Refraction Of Light Through Prism.

Laws Governing Refraction in a Glass Slab

The behavior of light as it moves across media boundaries in a glass slab is described by the laws of refraction. The primary law, known as Snell’s Law, states:

$n_1 \sin i = n_2 \sin r$

Here, $n_1$ and $n_2$ denote the refractive indices of the two media (air and glass), $i$ is the angle of incidence, and $r$ is the angle of refraction. For glass slabs, the refractive index of air is taken as approximately 1, while glass is typically between 1.5 and 1.6.

At each interface, Snell’s Law must be applied to determine the refraction angles. For further clarity on sign conventions, refer to Sign Convention In Lenses.

Lateral Displacement in a Glass Slab

Lateral displacement is the perpendicular distance between the original path of the incident ray and the emergent ray, as the light exits the glass slab. This effect occurs due to the parallel-sided nature of the slab.

The mathematical expression for lateral displacement ($d$) is given by:

$d = t \times \dfrac{\sin(i - r)}{\cos r}$

where $t$ is the slab thickness, $i$ is the angle of incidence, and $r$ is the angle of refraction. Each parameter must be clearly defined and identified in examination calculations.

Stepwise Derivation of Lateral Displacement

To derive the formula for lateral displacement, consider a ray of light entering and exiting the opposite faces of a rectangular glass slab. Using geometric relations and the laws of refraction, the lateral displacement is deduced through trigonometric analysis of the internal path and angles.

The emergent ray is parallel to the incident ray, but not along the same line, indicating displacement but no angular deviation. This is a hallmark feature of refraction through a rectangular slab, distinguishing it from other optical elements.

Solved Example: Lateral Displacement Calculation

Given a glass slab with a thickness of 1.0 cm, an angle of incidence of $45^\circ$, and a refractive index of 1.5. First, calculate the angle of refraction ($r$) using Snell’s Law: $1 \cdot \sin 45^\circ = 1.5 \cdot \sin r$. Solving this yields $r \approx 28^\circ$.

Substitute the values: $d = 1.0 \times \dfrac{\sin(45^\circ - 28^\circ)}{\cos 28^\circ} \approx 0.37 \ \mathrm{cm}$. This value represents the lateral shift of the emergent ray relative to the incident ray path.

Importance and Applications in Optics

The refraction of light through glass slabs is essential for understanding image formation in optical instruments, instrument glass windows, and the construction of precise scientific devices. Mastery of this topic is crucial for the optics portion of JEE Main.

Distinguishing between lateral displacement in slabs and deviation in prisms is necessary to solve ray diagram questions accurately. For differences between various optical elements, consult Difference Between Mirror And Lens.

Precautions and Common Mistakes

It is essential to label the normal, incident, and emergent rays accurately in diagrams. Both refractions at the slab faces must be considered. The emergent ray is always parallel to the incident ray, a feature unique to rectangular slabs.

• Account for two refractions in the slab
• Use correct sign conventions
• Angles must be measured consistently
• Do not confuse shift with angular deviation

Care must be taken with units and angle measurements while performing calculations. For topics related to measurement and velocity in optics, refer to Velocity Of Object And Image.

Relevance in Experimental Physics and Simulation

Refraction through a glass slab is commonly explored using classroom experiments and simulations at the school level. The results validate theoretical predictions about lateral displacement and parallel emergence of rays.

In practical examinations, accurate ray diagrams and identification of relevant angles are necessary for full marks. Additional practice can be obtained from simulation activities and practical manuals. Further explanations on light-matter interactions are available at Photoelectric Effect.