a. Ray optics and Optical instruments
Some basic properties of light
- Light travels with a constant speed in vacuum i.e. c= 3 × 108 m/s
- Rectilinear propagation- Light travels in a straight line
- Ray- The path of light is called a ray
- Beam- Bundle of rays is called beam •
• halo
Reflection of light (PYQ 2020, 2018, 2016, 2014, 2011)
Laws of reflection
1st law- The angle of incidence (i) is equal to the angle of reflection (r)
2nd law- The incident ray, the reflected ray and the normal, at the point
Of incidence, all lie in the same plane.
Sign convention
We follow the system of cartesian sign conventions-
- All distances are measured from the pole or the mirror or optical center of the lens
- The direction of incident light is taken as positive and the opposite direction is taken as negative
- The distances measured upwards w.r.t. the x-axis and perpendicular to the principal axis are positive and the
heights measured downwards are negative.
Focal length of spherical mirrors
Principal focus- A paraxial ray of light after reflection converge or appear
to diverge from a point after reflection form a concave or convex mirror
respectively. This point F is called the principal focus of the mirror.
Focal plane- If the paraxial rays of light were incident making some angle
with the principal axis, the reflected rays converge or appear to diverge
from a point in a plane through F normal to the principal axis. This is
called the focal plane of the mirror.
Focal length- The distance between the focus F and pole P of a mirror is
called the focal length of the mirror (f).
Radius of curvature- The radius of the sphere of which the mirror is a part
Of is called the radius of curvature of the mirror. (R)
Note: We will make all calculations and formulas for paraxial rays i.e. rays
which are incident at points close to the pole and make small angles with
the principal axis.
, Relation between focal length and radius of curvature
Let the center of curvature of the mirror be C. Consider a ray parallel to the principal axis, incident at M. let angle of
incidence be θ.
In
(External angle property)
Also,
Gold
Also, if
For
dis
The Mirror equation (PYQ 2020, 2018, 2016, 2011)
If rays emanating from a point actually meet at a point after reflection and/or refraction, that point is called the
image of the point. The image is real if the rays actually converge at a point and it is virtual if the do not actually
meet but appear to diverge from a point when produced backwards.
Rules for drawing Ray diagrams
1. Rays of light parallel to the principal axis pass through the principal focus after reflection.
2. The rays of light passing through the center of curvature of a concave mirror or appearing to pass through it for a
convex mirror retrace their path after reflection.
3. Rays passing through or appearing to pass through the principal focus of a concave and convex mirror respectively,
become parallel to the principal axis after reflection.
4. Rays incident at any angle at the pole, follow laws of reflection.
The mirror equation is the relation between the object distance (u), image distance (v) and focal length (f).
Consider the following ray diagram for object AB-
Also,
Subs:tu:ng values from figure considering sign conven:ons
, Linear Magnification (m) (PYQ 2018, 2016, 2014)
It is defined as the ratio of the height of the image(h’) to that of the object (h) (h and h’ are taken positive or
negative according to the sign convention)
h
ti
Subs:tu:ng values from figure considering sign conven:ons
Magnification Image type
Negative inverted
Positive Virtual
>1 Magnified
<1 Diminished
Image formation for concave mirror
Object Position Image Position Nature
1. At Infinity At Focus Real, inverted and diminished
2. Between infinity and C Between F and C Real, inverted and diminished
3. At C At C Real, inverted and same sized
4. Between F and C Between c and infinity Real, inverted and magnified
5. At F At infinity Real, inverted and magnified
6. Between F and P Behind the mirror Virtual, erect and magnified
Image formation for convex mirror
Object Image Nature
1. At infinity At F behind the mirror Virtual, erect and diminished
2. Anywhere else Behind the mirror Virtual, erect and diminished
Some basic properties of light
- Light travels with a constant speed in vacuum i.e. c= 3 × 108 m/s
- Rectilinear propagation- Light travels in a straight line
- Ray- The path of light is called a ray
- Beam- Bundle of rays is called beam •
• halo
Reflection of light (PYQ 2020, 2018, 2016, 2014, 2011)
Laws of reflection
1st law- The angle of incidence (i) is equal to the angle of reflection (r)
2nd law- The incident ray, the reflected ray and the normal, at the point
Of incidence, all lie in the same plane.
Sign convention
We follow the system of cartesian sign conventions-
- All distances are measured from the pole or the mirror or optical center of the lens
- The direction of incident light is taken as positive and the opposite direction is taken as negative
- The distances measured upwards w.r.t. the x-axis and perpendicular to the principal axis are positive and the
heights measured downwards are negative.
Focal length of spherical mirrors
Principal focus- A paraxial ray of light after reflection converge or appear
to diverge from a point after reflection form a concave or convex mirror
respectively. This point F is called the principal focus of the mirror.
Focal plane- If the paraxial rays of light were incident making some angle
with the principal axis, the reflected rays converge or appear to diverge
from a point in a plane through F normal to the principal axis. This is
called the focal plane of the mirror.
Focal length- The distance between the focus F and pole P of a mirror is
called the focal length of the mirror (f).
Radius of curvature- The radius of the sphere of which the mirror is a part
Of is called the radius of curvature of the mirror. (R)
Note: We will make all calculations and formulas for paraxial rays i.e. rays
which are incident at points close to the pole and make small angles with
the principal axis.
, Relation between focal length and radius of curvature
Let the center of curvature of the mirror be C. Consider a ray parallel to the principal axis, incident at M. let angle of
incidence be θ.
In
(External angle property)
Also,
Gold
Also, if
For
dis
The Mirror equation (PYQ 2020, 2018, 2016, 2011)
If rays emanating from a point actually meet at a point after reflection and/or refraction, that point is called the
image of the point. The image is real if the rays actually converge at a point and it is virtual if the do not actually
meet but appear to diverge from a point when produced backwards.
Rules for drawing Ray diagrams
1. Rays of light parallel to the principal axis pass through the principal focus after reflection.
2. The rays of light passing through the center of curvature of a concave mirror or appearing to pass through it for a
convex mirror retrace their path after reflection.
3. Rays passing through or appearing to pass through the principal focus of a concave and convex mirror respectively,
become parallel to the principal axis after reflection.
4. Rays incident at any angle at the pole, follow laws of reflection.
The mirror equation is the relation between the object distance (u), image distance (v) and focal length (f).
Consider the following ray diagram for object AB-
Also,
Subs:tu:ng values from figure considering sign conven:ons
, Linear Magnification (m) (PYQ 2018, 2016, 2014)
It is defined as the ratio of the height of the image(h’) to that of the object (h) (h and h’ are taken positive or
negative according to the sign convention)
h
ti
Subs:tu:ng values from figure considering sign conven:ons
Magnification Image type
Negative inverted
Positive Virtual
>1 Magnified
<1 Diminished
Image formation for concave mirror
Object Position Image Position Nature
1. At Infinity At Focus Real, inverted and diminished
2. Between infinity and C Between F and C Real, inverted and diminished
3. At C At C Real, inverted and same sized
4. Between F and C Between c and infinity Real, inverted and magnified
5. At F At infinity Real, inverted and magnified
6. Between F and P Behind the mirror Virtual, erect and magnified
Image formation for convex mirror
Object Image Nature
1. At infinity At F behind the mirror Virtual, erect and diminished
2. Anywhere else Behind the mirror Virtual, erect and diminished
