Optics Notes

12.1 Reflection of Light

• Normal: Imaginary line perpendicular to the reflecting surface at the point of incidence.

• Angle of Incidence (\i): The angle between the incident ray and the normal.

• Angle of Reflection (\r): The angle between the reflected ray and the normal.

How We Represent Light

Light is an electromagnetic wave that undergoes reflection, allowing us to see objects. Luminous objects emit their own light (e.g., lamp, fire), while non-luminous objects reflect light from a source (e.g., a wall picture).

In physics, light paths are represented by straight lines with arrows, called light rays, indicating direction. A beam of light is a bundle of light rays, which can be parallel, convergent, or divergent.

• Parallel light rays: Represent light from a distant object (e.g., the Sun).

• Divergent light rays: Represent light from a nearby object.

Terms Describing Reflection

• Reflection: Rebounding of light at a surface.

• Incident Ray: Light ray that hits the reflecting surface.

• Point of Incidence: Point where the incident ray hits the reflecting surface.

• Reflected Ray: Light ray that bounces off the reflecting surface.

Law of Reflection

The angle of incidence (\i) is equal to the angle of reflection (\r), i.e., \i = r.

Characteristics of a Plane Mirror Image

• Same size as the object.

• Laterally inverted (left and right are reversed).

• Upright.

• Virtual (cannot be captured on a screen; light rays do not meet at the image position), which is opposite to a real image.

• Same distance from the mirror as the object.

Note: A real image can be captured on a screen, and light rays meet at the image position.

Ray Diagram for a Point Object

1. Locate the image (I) behind the mirror, ensuring it's the same perpendicular distance from the mirror as the object (O) is in front of it.

2. Draw reflected rays from the image (I) to the eye.

3. Draw incident rays from the object (O) to the points of incidence on the mirror surface.

4. Use dotted lines for rays behind the mirror and solid lines with arrowheads for rays reflected off the mirror.

5. Ensure the angle of incidence equals the angle of reflection for each ray.

Ray Diagram for an Extended Object

An extended object is treated as multiple points. Repeat the steps for a point object for several points on the extended object, especially the extreme points.

Applications of Mirrors

• Vision Testing: Mirrors are used in small rooms to simulate distance in eye charts.

• Periscope: Two plane mirrors inclined at 45° to see over obstacles.

• Blind Corner Mirror: Curved mirrors in shops or on roads to see around corners.

• Instrument Scale: Mirrors below pointers to avoid parallax error.

12.2 Refraction of Light

• Refraction: Bending of light as it passes from one optical medium to another.

• Normal: Imaginary line perpendicular to the refracting surface at the point of incidence.

• Angle of Incidence (\i): Angle between the incident ray and the normal.

• Angle of Refraction ($r$): Angle between the refracted ray and the normal.

Refractive Index and Speed of Light

Light travels at different speeds in different transparent materials (optical media). For instance, it travels at $3.0 \times 10^8$ m/s in air and $2.0 \times 10^8$ m/s in glass. This change in speed causes the bending of light, known as refraction.

Light travels fastest in a vacuum and slows down in optically denser media (e.g., glass, water).

Snell's Law

For two given media, the ratio of the sine of the angle of incidence (\i) to the sine of the angle of refraction ($r$) is a constant:

$\frac{\sin i}{\sin r} = \text{constant}$

The refractive index ($n$) is the ratio of the speeds of light in two different regions. Specifically, it's the ratio of the speed of light in a vacuum ($c$) to the speed of light in the medium ($v$):

$n = \frac{c}{v}$

A higher refractive index indicates slower light travel in the medium.

For light traveling from a vacuum to an optical medium:

$n = \frac{\sin i}{\sin r}$, where $i$ is the angle of incidence in a vacuum and $r$ is the angle of refraction in the medium.

A higher refractive index means a smaller angle of refraction ($r$), indicating more bending towards the normal.

Because the speed of light in air is very close to the speed of light in a vaccum, for most purposes, we can approximate:

$n = \frac{\text{speed of light in air}}{\text{speed of light in medium}}$

Daily Phenomena and Applications

• Objects in water appear bent due to refraction of light from the immersed part when it travels from water to air.

• Swimming pools appear shallower because of refraction.

12.3 Total Internal Reflection

Conditions for Total Internal Reflection

Total internal reflection occurs when light passes from an optically denser to a less dense medium.

• Critical Angle: When the angle of incidence is larger than the critical angle ($c$), the light ray reflects off the surface. There is no refraction at the boundary.

• The light ray strikes its boundary with an optically less dense medium.

• The angle of incidence is greater than the critical angle of the optically denser medium.

Determining Critical Angle

Given the refractive index ($n$) of a transparent material, the critical angle ($c$) can be found using:

$n = \frac{1}{\sin c}$

Applications of Total Internal Reflection

• Glass Prisms: Used in optical instruments like binoculars and periscopes to reflect light.- Binoculars use prisms to reduce size and rectify inverted images.

  • Periscopes can use prisms instead of plane mirrors for clearer images.

  • SLR cameras use pentaprisms to allow photographers to see the exact image to be captured.

• Optical Fibers: Transmit data over long distances using total internal reflection. They consist of a core with a high refractive index coated with a material of a lower refractive index.

Advantages of Optical Fibers over Copper Wires

• Higher carrying capacity.

• Less signal degradation.

• Lightweight.

• Lower cost.

Medical Applications

• Endoscopes use optical fibers to see inside hollow organs.

12.4 Refraction by Thin Lenses

A lens is a piece of clear plastic or glass with curved surfaces, used in cameras, spectacles, projectors, etc.

• Converging Lens: Thicker in the center, causes light rays to converge to a point.

• Diverging Lens: Thinner in the center, causes light rays to diverge from a point.

Terms Describing a Thin Converging Lens

• Principal Axis: Horizontal line passing through the optical center of the lens, perpendicular to the vertical plane of the lens.

• Optical Center (C): Midpoint between the surfaces of the lens on its principal axis. Rays passing through the optical center are not refracted.

• Focal Point (F): Point at which all rays parallel to the principal axis converge after refraction. A lens has two focal points, one on each side.

• Focal Length (f): Distance between the optical center (C) and the focal point (F).

• Focal Plane: Plane that passes through the focal point (F) and is perpendicular to the principal axis.

Ray Diagrams for Converging Lenses

• Any light ray passing through the optical center (C) of a lens is not refracted.

• Any light ray parallel to the principal axis of a lens will converge at the focal point (F).