Chapter 12: Geometrical Optics

Definition: When light travelling in a certain medium falls on the surface of another medium, a part of it turns back in the same medium. This is called reflection of light.

• Regular Reflection: Occurs on smooth surfaces (e.g., plane mirror). Rays reflect in one direction.
• Irregular (Diffuse) Reflection: Occurs on rough surfaces. Rays reflect in many directions.

Laws of Reflection:

1. The incident ray, the reflected ray, and the normal all lie in the same plane.
2. The angle of incidence is equal to the angle of reflection ($i=r$).

A mirror whose polished, reflecting surface is a part of a hollow sphere of glass or plastic is called a spherical mirror.

Types:

• Concave Mirror: Inner curved surface is reflecting. It converges light rays to a real focus. Forms both real and virtual images.
• Convex Mirror: Outer curved surface is reflecting. It diverges light rays from a virtual focus. Always forms virtual, erect, and diminished images.

Terminology:

• Pole (P): Midpoint of the curved surface.
• Centre of Curvature (C): Centre of the sphere of which the mirror is a part.
• Radius of Curvature (R): Radius of the sphere.
• Principal Axis: Line joining C and P.
• Principal Focus (F): Point where parallel rays converge (concave) or appear to diverge from (convex).
• Focal Length (f): Distance between P and F. Related to radius by $f = R/2$.

The relationship between object distance $p$, image distance $q$, and focal length $f$ of the mirror.

\frac{1}{f} = \frac{1}{p} + \frac{1}{q}

Sign Conventions:

• Object Distance (p): Positive for real object, Negative for virtual object.
• Image Distance (q): Positive for real image, Negative for virtual image.
• Focal Length (f): Positive for Concave Mirror, Negative for Convex Mirror.

Definition: The bending of light as it passes from one transparent medium into another is called refraction. It occurs due to change in speed of light.

Laws of Refraction:

1. Calculated rays lie in the same plane.
2. Snell's Law: The ratio of sine of angle of incidence to sine of angle of refraction is constant. $n = \frac{\sin i}{\sin r}$

Refractive Index (n): Ratio of speed of light in vacuum ($c$) to speed of light in medium ($v$). $n = c/v$.

Total Internal Reflection: When incidence angle in denser medium exceeds critical angle, no refraction occurs; all light reflects back. Applications include Optical Fibres (Light Pipe, Endoscope) and Prisms (Periscope, Binoculars).

A transparent material with two surfaces, at least one curved.

• Convex (Converging) Lens: Thicker at centre. Converges light to a real focus.
• Concave (Diverging) Lens: Thinner at centre. Diverges light from a virtual focus.

Power of a Lens: Reciprocal of focal length in metres. Unit: Dioptre (D). $P = 1/f$

Lens Formula: Same as mirror formula: $\frac{1}{f} = \frac{1}{p} + \frac{1}{q}$

• Camera: Uses convex lens to form real, inverted, diminished image on film.
• Slide Projector: Uses concave mirror and condenser lenses. Slide placed between $F$ and $2F$ to form real, inverted, magnified image.
• Simple Microscope (Magnifying Glass): Convex lens used with object within focal length. Forms virtual, erect, magnified image. ($M = 1 + d/f$).
• Compound Microscope: Two convex lenses. Objective (short $f$) forms real magnified image. Eyepiece (longer $f$) acts as magnifying glass. High magnification.
• Telescope: Refracting telescope uses two lenses. Objective (long $f$) collects light; Eyepiece magnifies.

Acts like a camera. Retina acts as film. Iris controls Pupil size. Eye lens changes focal length (Accommodation) to focus objects.

• Near Point: Closest distance for distinct vision (~25 cm).
• Far Point: Farthest distance (Infinity for normal eye).

Defects of Vision:

• Nearsightedness (Myopia): Can see near, not far. Image formed in front of retina. Corrected with Concave Lens.
• Farsightedness (Hypermetropia): Can see far, not near. Image formed behind retina. Corrected with Convex Lens.