Geometrical Optics.PDF

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Geometrical Optics
Preparedby : Viral Nagar

Prepared By Viral Nagar ©
Lecture Flow
1
• Geometrical Optics
2
• Reflection of Light
3
• Plane Mirror
4
• Spherical Mirror
5
• Combination of Mirror
Tuesday, May 3, 2022
Standard – 12th Science Subject – Physics Ray Optics 2

Geometrical Optics
• The study of light in which light is considered as moving along the
straight line as a ray.
• A ray has a direction of its propagation.
Parallel Beam Divergent Beam Convergent Beam

Reflection

Reflection (Continue)
1. What will happen to ray when it incidents normal to the surface?
2. Due to reflection, Which quantities will not be affected? Which
quantity will get affected?
wavelength, frequency, speed – No change
Intensity of light (IαA2) - decreases

Plane Mirror

Deviation Angle

Rotation of a Mirror

Image formed by Plane Mirror

Concept – Quiz - 1
▪ Locate the image. Calculatedistance between object & image.

▪ For given clock time 8:12, what is the time shown by the image in plane
mirror.

Concept – Quiz-3
▪ How the Plane mirror is arranged with horizontal in order to obtain
vertical image for given object ?

Relation between velocity of object and image in plane mirror

Example
▪ An object moves with 5 m/s towards right while the mirror moves with
1 m/s towards the left as shown. Find the velocity of image.

Example
▪ In the situation shown in figure, find the velocity of image.

Example
▪ Find out deviation angle.
Angle of deviation = 90°

Example
• Find out deviation angle after first reflection, second reflection. Also
find total deviation angle.

Example

Image formed by two plane mirrors
❖Images due to parallel plane mirrors
▪ Total numberof images = ∞.

❖Images due to inclined plane mirrors

Example

Spherical Mirror

Magnification
Transverse or Lateral Magnification Longitudinal Magnification

Example

Velocity in Spherical Mirror
(a) Object moving along principalaxis
(b) Object movingperpendicular to principalaxis
(c) Object moving parallel to Principalaxis :

Example
▪ Find velocity of image in the given figure.

Combination of Mirror

Lecture Flow
1
• Refraction
2
• Refraction at plane surface
3
• Refraction at curved surface
4
• Lens Maker Formula

Refraction (વક્રીભવન)
• Deviation or bending of light rays from their original path while
passing from one medium to another is called refraction.
• Speed of light & wavelength changes due to refraction.
• Frequency of light doesn’t change due to refraction.
• Refractive index of the medium relative to vacuum

Snell’s law

When light moves from denser to rarer medium it bends away from normal.
When light moves from rarer to denser medium it bends towards the normal.
𝜹 = 𝒊 − 𝒓
r<i

Example
❑ Find the angles r, r′, e and the total deviation after two refractions.

Plane Refraction
If n1= n4 then light rays in medium n1 and in
medium n4 are parallel.
n1 sin i1= n2 sin i2 = n3 sini3 = n4 sini4

Apparent depth & Normal shift
• If n (denser) = n , n (rarer) = n (air) = 1
• 𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ(𝑑′)
𝑟𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ (𝑑)
=
1
𝑛
• 𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ(𝑑′) =
𝑛
• 𝑁𝑜𝑟𝑚𝑎𝑙 𝑆ℎ𝑖𝑓𝑡 ∆𝑆 = 𝑑 − 𝑑′
= 𝑑 −
𝑑
𝑛
= 𝑑 1 −
1
𝑛
∆𝑆 = 𝑑 1 −
1
𝑛
𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ(𝑑′)
=
𝑛(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟)
𝑛(𝑜𝑏𝑗𝑒𝑐𝑡)
=
𝑛(𝑟𝑎𝑟𝑒𝑟)
𝑛(𝑑𝑒𝑛𝑠𝑒𝑟)

Real & Virtual height
𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ(𝑑′
)
=
=
d’ = µd

Example
𝑎𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ(𝑑′
)
=
=
∆𝑆 = 𝑑 − 𝑑′
= 𝑑 −
𝑑
𝑛
= 𝑑 1 −
1
𝑛
= 6 1 −
1
1.5
= 2 𝑐𝑚

Example

Velocity of image in plane refraction

Example

Lateral Shift
• The perpendicular distance between the incident ray and the emergent ray
is called lateral shift

Example
❑Find lateral shift for the given figure.

Total Internal Refraction

Conditions of T.I.R
(a) light is incidenton the interfacefrom denser medium.
(b) Angle of incidenceshould be greater than the criticalangle (i > c).

Optical Fibre

Condition for T.I.R in Optical Fibre

Refraction at the spherical Surface

Example

Example
❑Find out the position of the image formed and draw the appropriate ray
diagram.

Example
❑Find out the position where parallel rays will meet after coming out of the
sphere and draw the appropriate ray diagram.

Velocity of spherical refraction

Example

Lecture Flow
1
• Lens
2
• Lens Makers Formula & thin Lens
3
• Silvering of Lens
4
• Refraction through Prism

Lens
• Lens is a transparent medium bounded by two refrecting surfaces,
such that at least one surface is spherical.

Lens Formulas

Types of Lens

Lens Makers Formula

Thin Lens
Lateral Magnification m = v/u

Application of Lens makers Formula
Equi-Convexlens Plano Convexlens Equi-ConcaveLens Plano-Concave Lens

Lens in a liquid

Example
▪ The focal length of a convex lens in air is 10 cm. Find its focal length in water.
Assume µg =3 / 2 and µw = 4 / 3

Example
▪ Calculate the focal length of a biconvex lens in air if the radii of its surfaces are
60 cm and 15 cm. Refractive index of glass = 1.5

Cutting of Lens

Silvering of Lens

Example
The convex surface of a plane of convex lens is silver whose radius
of curvature is R. Find the focal length of the mirror thus formed.

Example

Prism
• Prism is a transparent medium bounded by refracting surfaces, such
that the incident surface and emergent surface are plane and non
parallel.

Refraction through Prism

Minimum Deviation

Maximum Deviation

Normal Incidence on a Prism

Grazing Emergence and TIR

Geometrical Optics.PDF

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