Reflection and Refraction of Light

• Light is essential for vision, and a study of its properties helps to explain the phenomena around us such as the twinkling of stars and rainbows.

Chapter Overview

• This chapter explores reflection and refraction using the concept of light traveling in straight lines, applying these principles to mirrors and lenses.

Reflection of Light

• A mirror, which is a highly polished surface, reflects most of the light incident on it.
• The laws of reflection state that the angle of incidence equals the angle of reflection, and all related rays lie on the same plane.
• These laws apply to all reflecting surfaces, including spherical ones.
• Plane mirrors always form virtual and erect images.
• The object and the images are the same distance behind and in front of the mirror respectively and are laterally inverted.

Spherical Mirrors

• A shining spoon can act as a curved mirror
• Spherical mirrors are curved mirrors with their reflecting surface forming a part of a sphere.
• Concave mirrors curve inwards to the centre of the sphere.
• Convex mirrors curve outwards
• The pole (P) is the center of the reflecting surface of a spherical mirror.

Key Terms of Spherical Mirrors

• The centre of curvature (C) isn't part of the mirror, but is the centre of the sphere with the mirror as a part.
• The radius of curvature (R) is the radius of that sphere which is twice the focal length.
• The principal axis is a straight line passing through the pole and the center of curvature.

Understanding Focal Length - Activity

• A concave mirror can focus sunlight to a bright spot, which is the real and inverted image of the Sun
• The heat from this spot will burn any material it is focused on
• Approximate focal length equates to the distance of the image that you can see from the mirror

Focal Point

• Rays parallel to the principal axis converge at the principal focus (F) in a concave mirror.
• Reflected rays appear to come from the principal focus (F) in a convex mirror.
• Focal length (f) is the distance between the pole and the principal focus.

Aperture

• The reflecting surface of a spherical mirror is largely and spherical.
• The reflecting surface has a circular line
• Aperture is the diameter of the circular outline of a spherical mirror.
• Only mirrors with an aperture much smaller than the radius of curvature are under consideration.
• R = 2f equates to the Radius of curvature being equal to twice the focal length for spherical mirrors. This relates to the principal focus lying between the pole and centre of curvature.

Image Formation

• The position and nature of an image can be determined.
• This is with reference to the object's position relative to P, F, and C.
• Images can be real or virtual, magnified, diminished, or of the same size.

Summarized Observations for Concave Mirrors

• At infinity: Image at F, highly diminished, real and inverted.
• Beyond C: Image between F and C, diminished, real and inverted.
• At C: Image at C, same size, real and inverted.
• Between C and F: Image beyond C, enlarged, real and inverted.
• At F: Image at infinity, highly enlarged, real and inverted.
• Between P and F: Image behind the mirror, enlarged, virtual and erect.

Ray Diagrams

• Representing images with ray diagrams which need only two rays to find the image position.
• Key rays are one parallel to the principal axis reflecting through the focus or diverging from it (convex), and the reverse. A ray through the center of curvature reflects back along the same path.
• A ray to pole P reflects obliquely, adhering to the laws of reflection.

Image Formation

• Images are formed using ray diagrams for the formation of images by a concave mirror for various positions of the object which is shown in figures

Uses of Concave Mirrors

• Concave mirrors are used in torches, vehicle headlights, shaving mirrors, dental exams and solar furnaces.

Convex Mirrors

• Convex Mirrors are also used for ray diagrams for the formation of images

Sign Convention for Mirrors

• The convex mirror provides full view of the image
• The New Cartesian Sign Convention is followed in order to observe how light reflects with a mirror
• The pole (P) acts as the origin and the principal asix acts as the x-axis
• The position of the object should be on the left had side of the mirror
• Distances should be measured from the mirrors' pole and the distances on the right are positive while the lefr are negative
• All distances are measured above perpendicular and these plus values can be seen along the positive y-axis
• This opposite can be said in order to find distances below which are measured as negative under the coordinate

Mirror Formula and Magnification

• Mirror Formula: 1/v + 1/u = 1/f
• Where:
• f = focal length
• v = image distance
• u = object distance
• Linear Magnification = h’/h = - v/u

Absolute Refractive Index

• absolute refractive index of a medium = (speed of light in medium / speed of light in vacuum = number of lambda)

Refraction of Light

• Refraction is the bending of light as it passes from one medium to another.
• This explains the apparent rising of tank bottoms or displacement of objects in water.
• The degree of displacement varies by medium.

Refractive Index Explained

• Medium ability to refract to a point or to spread light.
• An oblique ray changes direction, bending towards the normal when entering a denser medium and away from normal when entering a rarer medium.

Laws of Refraction:

• (i) Incident and refracted rays, and the normal, lie in the same plane.
• (ii) Snell's Law: sin i / sin r = constant
• Where: i = angle of incidence, r = angle of refraction

Absolute Nature of Refractive Index

• Absolute nature is directly proportional to refractive index
• Light travels fastest in a vacuum
• Refractive index = speed of light in vacuum ( c )/ speed of light in medium "nm = c/v "

Refractive Index

• Refraction depends on change in light speed between media. Higher refractive index means lower speed.
• Optically denser doesn't mean greater mass density; it refers to a higher refractive index.
• A rarer optic bends from normal when traveling from medium to medium while a denser optic bends towards a normal in medium
• Example: Kerosene > Water > Diamond > others

Spherical Lenses

• Transparent material bound by two surfaces
• Spherical material made to form a less
• Concave Lens are thicker at the middle than edges which diverge light also converging light
• Lenses are bound by 2 spherical surfaces that curve
• Each center is known as a center of curvature and and marked with "C" and are an imaginary straight line

Conventions for Lenses

• O marks an optical centre
• Centre is one of the primary focal points
• F marks the principal focus and "F1 and F2" represents 2 principal foci
• Focal length equates to small "F" for the focal length letter

Focal Relationships

• Parallel rays of light converge or diverge at a lens's principal focus
• There are two principal foci of a lens, on either side, represented by "F1 and F2"
• Focal Length: the distance of the "P", principal focus, from the mirror.
• focal_leangth = "f" can be found experimentally.

Ray Diagrams

• You may not ever see your actual f stops or the aperture because they are more theoretical
• Need 2 rays to determine image -A ray to pass by a convex is similar to "F" but to concave it diverges

Important Key Facts

• A convex lens will reach a primary focus at the side of the lens the light can't reach. On the opposite end the light is divergently pointing in the direction it was supposed to travel, on a convex, it appears at the place they used to travel from
• Image Formation Formula: 1 / v − 1 / u = 1 / f
• Spherical Magnification Formula: h’/h = - v/u

Power of a Lens

• Degree of convergence, or divergence of the light rays can be achieved by a lens power in terms of "P", the measure
• P = 1/ f

Power Conventions

• Power measures the size of F, focal length and is measured in "D". dioptre
• "D" measures lenses
• A convex lens has a positive lens, while a concave lens has a negative length
• Some lenses require multiple lenses or a series used for lens design across scientific instruments