Refraction

The figure shows a horizontal interface (the boundary between two transparent media). The upper half is medium 1 (air, rarer) and the lower half is medium 2 (shaded, denser). At the point where the incident ray meets the interface, a dashed normal is drawn perpendicular to the interface.

Three rays are shown:

• Incident ray: comes from the upper left, making an angle $i$ with the normal.
• Reflected ray: goes back into medium 1 on the other side of the normal, making the same angle $i$ with the normal (law of reflection).
• Refracted ray: enters medium 2, bending toward the normal, making an angle $r$ with the normal (where $r < i$ because medium 2 is denser).

All three rays and the normal lie in the same plane.

Physical idea: When light passes obliquely from a rarer to a denser medium, its speed decreases, causing the ray to bend toward the normal. The figure illustrates both reflection (a part of the light returns) and refraction (the rest enters the second medium with a changed direction).

Key formula developed from this figure is Snell’s law:

where:

• $i$ = angle of incidence (between incident ray and normal)
• $r$ = angle of refraction (between refracted ray and normal) …

What the diagram shows

The figure depicts a rectangular glass slab with parallel top and bottom faces, drawn as a tilted parallelogram to indicate its thickness. An incident ray approaches the top face at an angle $i_1$ measured from the normal (a dashed line perpendicular to the surface). Inside the glass, the ray bends toward the normal, making an angle $r_1$ with the normal — this is the refracted ray. It travels straight through the slab until it meets the bottom face, where it emerges into air. At the bottom interface, the ray bends away from the normal, and the angle of emergence $r_2$ equals the original angle of incidence $i_1$. The emergent ray is therefore parallel to the incident ray but shifted sideways by a distance called the lateral shift. A dashed extension of the incident ray shows the path it would have taken if the slab were absent, making the sideways displacement visible.

Physical idea

The figure illustrates that a parallel-sided slab does not change the direction of a light ray — it only displaces it laterally. This happens because refraction at the top surface bends the ray toward the normal (since glass is optically denser than air), and refraction at the bottom surface bends it away from the normal by the same amount, restoring the original direction. The lateral shift depends on the slab thickness, the angle of incidence, and the refractive index of the glass.

Key formula

The lateral shift $d$ is given by:

where:

• $t$ = thickness of the slab,
• $i_1$ = angle of incidence at the top face, …

Figure 9.10: Apparent Depth for Normal and Oblique Viewing

The figure has two side-by-side panels, both showing a vertical cross-section of a tank of water. The water is shaded, and the bottom of the tank is a horizontal line. An object O sits on the bottom. In each panel, the water surface is a horizontal line at the top of the shaded region. A normal (a dashed vertical line) is drawn at the point where a ray from O meets the surface.

Panel (a): Normal viewing

A single ray leaves O nearly vertically upward. At the water–air interface, it refracts away from the normal (since water is optically denser than air, so the ray bends away from the normal when entering the rarer medium). The actual refracted ray continues into air. A dashed line extends the refracted ray backward (into the water) until it meets the vertical line through O. This intersection point is labelled I — the apparent position of the object. The vertical distance from the water surface down to I is labelled apparent depth ($h_1$), and the distance from the surface down to O is labelled real depth ($h_2$). The figure shows $h_1 < h_2$, so the bottom appears raised.

Panel (b): Oblique viewing

Two rays leave O at different angles, both oblique (not vertical). Each ray refracts at the surface, bending away from the normal. The backward extensions of the two refracted rays (dashed lines) intersect at a point I that is shifted sideways and raised relative to O. The apparent depth is again less than the real depth, but the image is also displaced horizontally.

Physical idea

The figure teaches that when an object is viewed from a rarer medium (air) into a denser medium (water), the light rays bend away from the normal upon exiting the water. The brain interprets the rays as having travelled in straight lines, so it projects the object to a point I that is shallower than the actual object O. This is why a swimming pool or a tank of water looks shallower than it really is.

Key formula (for near-normal viewing)

For viewing nearly along the normal (small angles), the apparent depth $h_1$ and real depth $h_2$ are related by the refractive index $n$ of water (with respect to air):

where: …