Reflection at a Spherical Surface
Passenger-side mirror of a car is a convex spherical mirror, which curves outward. It makes
images appear smaller and farther away than they actually are. This helps drivers see a wider
field of view, improving awareness of their surroundings. Convex mirrors are commonly used
for safety and visibility in many practical applications.
1. Types of Spherical Mirrors
Concave Mirror: Curves inward;
reflects light rays to converge.
Convex Mirror: Curves outward;
reflects light rays to diverge.
2. Law of Reflection
Formula:θᵢ = θᵣ (Angle of incidence = Angle of reflection)
The incident ray, reflected ray, and normal all lie in the
same plane.
The law of reflection is what allows us to see an image of
ourselves when we look in a mirror. The location at which
the reflected light rays come to a point, or can be traced to a
point, is where the image is located. This is called the
image location.
Ray diagram of reflection at a spherical surface
1. Parallel rays of light – Light rays that travel in the
same direction and do not meet.
2. Optical axis – An imaginary line that defines the path
along which light travels through the center of the lens.
3. Principal axis – A straight line passing through the
optical center and focal point; the main reference line in
ray diagrams.
4. Focal point (F) – The point where parallel rays of light
appear to diverge (for a concave lens) after passing
through the lens.
5. Optical centre (O) – The center point of the lens where
light rays pass through without bending.
6. Focal length (f) – The distance between the optical
center and the focal point.
Key Notes:
An image that forms in front of the mirror where the light rays can reach, is a real image. If the
image location is behind the surface of the mirror where the light does not reach, then it is a
virtual image.
An important property of these images is that a real image can be projected onto a screen but a
virtual image cannot.
We calculate the image location using the mirror equation:
It is important to note that any distance behind the surface of the mirror is considered a
negative distance. For example, the distance to the focus for a convex mirror is a negative
distance. The image distance is considered positive if the image is in front of the mirror and
negative if it is behind it. The object's distance to a mirror is always considered positive.
We determine the size of the image and whether it is upright or inverted using the
magnification equation:
Reflection of Light at Concave Mirror
The image created by reflection of light from a concave mirror can be real or virtual, depending
on the location of the object with respect to the mirror. The image of an object located beyond
the center of curvature of the mirror will be real, inverted, and reduced in size, as we can see
by tracing the rays from the object.
Reflection of Light at a Convex Mirror
A convex mirror always produces upright, virtual images. For an object that is infinitely far
away, the image location is at the focus and is the smallest image possible. An object placed at
any distance between infinity and the mirror's surface will produce an image that is still reduced
in size and is located between the mirror and the focus.
Refraction at a Spherical surface
Refraction is the bending of light as it passes from one transparent medium to another due to a
change in speed.At spherical surfaces, refraction occurs when light passes through curved
boundaries (convex or concave) between two media.
Laws of Refraction
Plane surface
1. Incident ray, normal, and refracted ray lie on the
same plane.
2. The ratio of the sine of the angle of incidence to
the sine of the angle of refraction is constant (Snell’s
Law): n₁ sin𝜃₁ = n₂ sin𝜃₂
where:
n₁, n₂ = refractive indices
𝜃₁ = angle of incidence
𝜃₂ = angle of refraction
Refractive Index (n).
Measures how much light bends when entering a
medium.
n = c / v, where:
c = speed of light in air
v = speed of light in the medium
Spherical surface
Refraction at a Spherical surface
Spherical surfaces are an integral part of the sphere. If you want to know about a common
spherical surface, you will notice the spherical mirrors, a great example. Convex and concave
are two common spherical surfaces. Convex is a surface that has curved outwards. A convex
lens supports refraction from rarer to denser medium at a convex spherical refracting surface.
Spherical Surfaces and Lenses
Spherical surfaces resemble segments of a
sphere.
Two types:
Concave Surface: Curves inward (converging
surface).
Convex Surface: Curves outward (diverging
surface).
Spherical Lenses: Made of two spherical
surfaces.
Convex Lens: Converges light rays.
Concave Lens: Diverges light rays
Key Takeaways:
Reflection at a Spherical Surface
 Passenger-side mirrors are convex spherical mirrors, used for wider field of view and
safety.
Types of Spherical Mirrors
 Concave Mirror: Curves inward; converges light rays.
 Convex Mirror: Curves outward; diverges light rays.
Law of Reflection
 θᵢ = θᵣ (angle of incidence equals angle of reflection).
 Incident ray, reflected ray, and normal lie in the same plane.
 Image formation depends on where the reflected rays meet (real vs. virtual images).
Ray Diagram Components
 Parallel rays: Same direction, no convergence.
 Optical/Principal Axis: Reference lines for light travel.
 Focal Point (F): Point where rays converge or appear to diverge.
 Optical Centre (O): Center point of the lens.
 Focal Length (f): Distance from optical centre to focal point.
Image Characteristics
 Real Image: In front of the mirror, projectable.
 Virtual Image: Behind the mirror, not projectable.
 Mirror Equation: Calculates image location.
 Magnification Equation: Determines size and orientation (upright/inverted).
Specific Cases
 Concave Mirror: Real or virtual image depending on object position.
 Convex Mirror: Always produces upright, virtual, reduced images.
Refraction at a Spherical Surface
Basic Principle
 Light bends when passing between different media due to speed change.
Laws of Refraction
 Incident ray, normal, and refracted ray lie in the same plane.
 Snell’s Law:
n1sinθ1=n2sinθ2
Refractive Index (n)
 n=c/v, where:
o c = speed of light in air
o v = speed of light in the medium
Spherical Surfaces and Lenses
 Spherical surfaces mimic segments of a sphere.
 Types:
o Concave Surface: Inward-curving, converges rays.
o Convex Surface: Outward-curving, diverges rays.
 Spherical Lenses are made from two spherical surfaces:
o Convex Lens: Converging
o Concave Lens: Diverging
Law Refraction
of Reflection