💡 Reflection and Refraction of Light
• Focal Length (f): Distance between the pole and the principal focus.
• Aperture: The diameter of the reflecting surface.
For spherical mirrors with small apertures, the relationship between the radius of curvature (R) and the
focal length (f) is:
R=2f R=2f
or
f=R2 f=2R
This means the principal focus lies midway between the pole and the center of curvature.
Ray Diagrams for Spherical Mirrors 📐
Rules for Making Ray Diagrams
1. Parallel Ray Rule
• Concave Mirror: A light ray parallel to the principal axis, after reflection, passes through
the focal point F.
• Convex Mirror: A light ray parallel to the principal axis, after reflection, appears to come
from the focal point F behind the mirror.
2. Focal Ray Rule
• Concave Mirror: A light ray passing through the principal focus after reflection emerges
parallel to the principal axis.
• Convex Mirror: A light ray directed towards the principal focus after reflection emerges
parallel to the principal axis.
3. Center of Curvature Ray Rule
• Concave Mirror: A light ray going from the object to the center of curvature retraces its
path back to the center of curvature after reflection.
• Convex Mirror: A light ray directed towards the center of curvature retraces its path after
reflection.
4. Oblique Ray Rule: A ray incident oblique to the principal axis towards the pole is reflected
obliquely, making equal angles with the principal axis.
Image Formation by a Concave Mirror
Object Position Image Position Image Size Image Nature
At Infinity At Focus (F) Highly Diminished Real and Inverted
Beyond C Between F and C Diminished Real and Inverted
At C At C Same as Object Real and Inverted
Between C and F Beyond C Enlarged Real and Inverted
At F At Infinity Highly Enlarged Real and Inverted
Between P and F Behind Mirror Enlarged Virtual and Erect
, Uses of Concave Mirrors
• Shaving mirrors
• Dentist mirrors
• Reflectors in torch lights and vehicle lights
Image Formation by a Convex Mirror
Object Position Image Position Image Size Image Nature
At Infinity At Focus (Behind) Highly Diminished Virtual and Erect
Between Infinity and Pole of Mirror Between P and F (Behind) Diminished Virtual and Erect
Uses of Convex Mirrors
• Rear-view mirrors in vehicles (provides an erect image and a wider field of view).
Sign Convention for Reflection by Spherical Mirrors ➕➖
The sign convention is a set of rules to determine the sign (positive or negative) of distances and
quantities.
• Object Placement: Always placed to the left of the mirror.
• Measurements from the Pole: All distances are measured from the mirror's pole.
• Direction of Measurement: All distances measured to the
Spherical Mirrors 🪞
Sign Conventions
When analyzing spherical mirrors, it's important to adhere to specific sign conventions:
• Distances measured to the right of the origin (along the positive x-axis) are
considered positive.
• Distances measured to the left of the origin (along the negative x-axis) are
considered negative.
• Heights measured above the principal axis (along the positive y-axis) are considered positive.
• Heights measured below the principal axis (along the negative y-axis) are
considered negative.
Mirror Formula
The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a spherical
mirror:
1v+1u=1f v1+u1=f1
Where:
• f is the focal length of the mirror
• v is the image distance
• u is the object distance
• Focal Length (f): Distance between the pole and the principal focus.
• Aperture: The diameter of the reflecting surface.
For spherical mirrors with small apertures, the relationship between the radius of curvature (R) and the
focal length (f) is:
R=2f R=2f
or
f=R2 f=2R
This means the principal focus lies midway between the pole and the center of curvature.
Ray Diagrams for Spherical Mirrors 📐
Rules for Making Ray Diagrams
1. Parallel Ray Rule
• Concave Mirror: A light ray parallel to the principal axis, after reflection, passes through
the focal point F.
• Convex Mirror: A light ray parallel to the principal axis, after reflection, appears to come
from the focal point F behind the mirror.
2. Focal Ray Rule
• Concave Mirror: A light ray passing through the principal focus after reflection emerges
parallel to the principal axis.
• Convex Mirror: A light ray directed towards the principal focus after reflection emerges
parallel to the principal axis.
3. Center of Curvature Ray Rule
• Concave Mirror: A light ray going from the object to the center of curvature retraces its
path back to the center of curvature after reflection.
• Convex Mirror: A light ray directed towards the center of curvature retraces its path after
reflection.
4. Oblique Ray Rule: A ray incident oblique to the principal axis towards the pole is reflected
obliquely, making equal angles with the principal axis.
Image Formation by a Concave Mirror
Object Position Image Position Image Size Image Nature
At Infinity At Focus (F) Highly Diminished Real and Inverted
Beyond C Between F and C Diminished Real and Inverted
At C At C Same as Object Real and Inverted
Between C and F Beyond C Enlarged Real and Inverted
At F At Infinity Highly Enlarged Real and Inverted
Between P and F Behind Mirror Enlarged Virtual and Erect
, Uses of Concave Mirrors
• Shaving mirrors
• Dentist mirrors
• Reflectors in torch lights and vehicle lights
Image Formation by a Convex Mirror
Object Position Image Position Image Size Image Nature
At Infinity At Focus (Behind) Highly Diminished Virtual and Erect
Between Infinity and Pole of Mirror Between P and F (Behind) Diminished Virtual and Erect
Uses of Convex Mirrors
• Rear-view mirrors in vehicles (provides an erect image and a wider field of view).
Sign Convention for Reflection by Spherical Mirrors ➕➖
The sign convention is a set of rules to determine the sign (positive or negative) of distances and
quantities.
• Object Placement: Always placed to the left of the mirror.
• Measurements from the Pole: All distances are measured from the mirror's pole.
• Direction of Measurement: All distances measured to the
Spherical Mirrors 🪞
Sign Conventions
When analyzing spherical mirrors, it's important to adhere to specific sign conventions:
• Distances measured to the right of the origin (along the positive x-axis) are
considered positive.
• Distances measured to the left of the origin (along the negative x-axis) are
considered negative.
• Heights measured above the principal axis (along the positive y-axis) are considered positive.
• Heights measured below the principal axis (along the negative y-axis) are
considered negative.
Mirror Formula
The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a spherical
mirror:
1v+1u=1f v1+u1=f1
Where:
• f is the focal length of the mirror
• v is the image distance
• u is the object distance
