The Reflection of Light: Mirrors

The Reflection of Light

LAW OF REFLECTION

The incident ray, the reflected ray, and the normal to the surface all lie in the same
plane, and the angle of incidence equals the angle of reflection.

Plane mirror
25.2 The Reflection of Light

In specular reflection, the reflected rays are parallel to each

other.
The Formation of Images by a Plane Mirror
The person’s right hand becomes
the image’s left hand.

The image has the following properties:

1. It is upright.
2. It is the same size as you are.
3. The image is as far behind the mirror
are you are in front of it.
4. It is laterally inverted.
5. It is virtual.
 The Formation of Images by a Plane Mirror
A ray of light from the top of the chess piece reflects from the mirror. To the eye, the ray
seems to come from behind the mirror. Because none of the rays actually emanate from
the image, it is called a VIRTUAL IMAGE.

Note: Image distance is equal to the object distance.

 Spherical Mirrors

If the inside surface of the spherical mirror is polished, it is a CONCAVE MIRROR. If the
outside surface is polished, is it a CONVEX MIRROR.

The law of reflection applies, just as it does for a plane mirror.

The PRINCIPAL AXIS of the mirror is a straight line drawn through the center and the
midpoint of the mirror.
 Spherical Mirrors

Light rays near and parallel to the principal axis are

reflected from the concave mirror and converge at the When paraxial light rays that are parallel to the
focal point. principal axis strike a convex mirror, the rays
appear to originate from the focal point.
The focal length is the distance between the focal point
and the mirror.
𝒇 = 𝑹/𝟐 𝒇 = −𝑹/𝟐
The Formation of Images by Spherical Mirrors
Ray tracing for concave mirrors

This ray is initially parallel to the

principal axis and passes through
the focal point.

This ray initially passes through

the focal point, then emerges
parallel to the principal axis.

This ray travels along a line that

The rays converge to the tip of the
passes through the center.
enlarged, inverted, real image.
 The Formation of Images by Spherical Mirrors
Ray tracing for concave mirrors

When an object is located between the focal point

and a concave mirror, an enlarged, upright, and
The rays converge to the tip of the virtual image is produced.
enlarged, inverted, real image.
The Formation of Images by Spherical Mirrors
Ray tracing for convex mirrors

Ray 1 is initially parallel to the principal

axis and appears to originate from the
focal point.

Ray 2 heads towards the focal point,

emerging parallel to the principal axis.

Ray 3 travels toward the center of The virtual image is diminished in size
curvature and reflects back on itself. and upright.
 The Formation of Images by Spherical Mirrors

The virtual image is diminished in size and upright.

Side mirrors use a Convex mirror to

https://www.physlink.com/education/askexperts/ae449.cfm
“compress” the view from the side.
25.6 The Mirror Equation and Magnification

f = focal length

do = object distance

di = image distance

m = magnificat ion
25.6 The Mirror Equation and Magnification

These diagrams are used

to derive the mirror equation.

1 1 1
+ =
do di f

hi di
m= =−
ho do
25.6 The Mirror Equation and Magnification

Summary of Sign Conventions for Spherical Mirrors

f is + for a concave mirror.
f is − for a convex mirror.

do is + if the object is in front of the mirror.

do is − if the object is behind the mirror.

𝑑𝑖 is + if the image is in front of the mirror (real image).

𝑑𝑖 is − if the image is behind the mirror (virtual image).

𝑚 is + for an upright image.

𝑚 is − for an inverted image.
25.6 The Mirror Equation and Magnification

Example 5 A Virtual Image Formed by a Convex Mirror

A convex mirror is used to reflect light from an object placed 66 cm in

front of the mirror. The focal length of the mirror is -46 cm. Find the location
of the image and the magnification.

1 1 1 1 1
= − = − = −0.037 cm−1
𝑑𝑖 𝑓 𝑑𝑂 −46 cm 66 cm

di = −27 cm

di
m=− =−
(− 27 cm)
= 0.41
do 66 cm
The Refraction of Light: Lenses and
Optical Instruments
CHAPTER 26
 The Index of Refraction
The speed of light in a vacuum is: Light travels through materials
𝒄 ≈ 𝟑. 𝟎𝟎 × 𝟏𝟎𝟖 𝐦Τ𝐬 at a speed less than its speed in
a vacuum.

DEFINITION OF THE INDEX OF REFRACTION

The index of refraction of a material is the ratio of the speed of

light in a vacuum to the speed of light in the material:

Speed of light in vacuum 𝒄

𝒏= =
Speed of light in the material 𝒗
Snell’s Law and the Refraction of Light
SNELL’S LAW OF REFRACTION

When light travels from a material with one index of

refraction to a material with a different index of
refraction, the angle of incidence is related to the angle
of refraction by

𝒏𝟏 𝐬𝐢𝐧 𝜽𝟏 = 𝒏𝟐 𝐬𝐢𝐧 𝜽𝟐
Snell’s Law and the Refraction of Light

https://studiousguy.com/laws-of-reflection-and-refraction/

https://www.sciencephoto.com/media/92425/view/refracted-light
Snell’s Law and the Refraction of Light – Example 1

Determining the Angle of Refraction

A light ray strikes an air/water surface at an angle of 46 degrees with
respect to the normal. Find the angle of refraction when the direction
of the ray is (a) from air to water and (b) from water to air.

𝒏𝟏 𝐬𝐢𝐧 𝜽𝟏 𝟏. 𝟎𝟎 𝐬𝐢𝐧 𝟒 𝟔∘
(a) 𝐬𝐢𝐧 𝜽𝟐 =
𝒏𝟐
=
𝟏. 𝟑𝟑
= 𝟎. 𝟓𝟒

𝜽𝟐 = 𝟑𝟑∘

𝒏𝟏 𝐬𝐢𝐧 𝜽𝟏 𝟏. 𝟑𝟑 𝐬𝐢𝐧 𝟒 𝟔∘
(b) 𝐬𝐢𝐧 𝜽𝟐 =
𝒏𝟐
=
𝟏. 𝟎𝟎
= 𝟎. 𝟗𝟔

𝜽𝟐 = 𝟕𝟒∘
26.2 Snell’s Law and the Refraction of Light

APPARENT DEPTH

Example 2 Finding a Sunken Chest

The searchlight on a yacht is being used to illuminate a sunken

chest. At what angle of incidence should the light be aimed?
26.2 Snell’s Law and the Refraction of Light

 2 = tan−1 (2.0 3.3) = 31

n2 sin  2 (1.33)sin 31

sin 1 = = = 0.69
n1 1.00

1 = 44
Total Internal Reflection
When light passes from a medium of larger refractive index into one of smaller
refractive index, the refracted ray bends away from the normal.

https://digg.com/video/laser-water-experiment
26.3 Total Internal Reflection

When light passes from a medium of larger refractive index into one
of smaller refractive index, the refracted ray bends away from the
normal.

n2
Critical angle sin  c = n1  n2
n1
26.3 Total Internal Reflection

Example 5 Total Internal Reflection

A beam of light is propagating through diamond and strikes the diamond-air

interface at an angle of incidence of 28 degrees. (a) Will part of the beam
enter the air or will there be total internal reflection? (b) Repeat part (a)
assuming that the diamond is surrounded by water.
26.3 Total Internal Reflection

 n2   1.00 
(a)  c = sin −1   = sin −1   = 24.4


 n1   2.42 

(b)  n2  −1  1.33 
 c = sin   = sin 
 
−1
 = 33.3


 n1   2.42 
Lenses
Lenses refract light in such a way that an image of the light source is formed.

With a converging lens, paraxial rays that are parallel to the principal axis converge to the focal point.

With a diverging lens, paraxial rays that are parallel to the principal axis appear to originate from the focal point.
 The Formation of Images by Lenses
IMAGE FORMATION BY A CONVERGING LENS

In this example, when the object is placed further than When the object is placed between F and 2F, the real image is
twice the focal length from the lens, the real image is inverted and larger than the object.
inverted and smaller than the object.

When the object is placed between F and the lens, the virtual image is upright and larger than the object.
The Formation of Images by Lenses
IMAGE FORMATION BY A DIVERGING LENS

A diverging lens always forms an upright, virtual, diminished image.

26.8 The Thin-Lens Equation and the Magnification Equation

1 1 1 hi di
+ = m= =−
do di f ho do
26.8 The Thin-Lens Equation and the Magnification Equation

Summary of Sign Conventions for Lenses

f is + for a converging lens.

f is − for a diverging lens.

do is + if the object is to the left of the lens.

do is − if the object is to the right of the lens.

di is + for an image formed to the right of the lens (real image).

di is − for an image formed to the left of the lens (virtual image).

m is + for an upright image.

m is − for an inverted image.
26.8 The Thin-Lens Equation and the Magnification Equation

Example 9 The Real Image Formed by a Camera Lens

A 1.70-m tall person is standing 2.50 m in front of a camera. The

camera uses a converging lens whose focal length is 0.0500 m.
(a) Find the image distance and determine whether the image is
real or virtual. (b) Find the magnification and height of the image
on the film.

1 1 1 1 1
(a) = − = − = 19.6 m −1
d i f d o 0.0500 m 2.50 m

di = 0.0510 m real image

di 0.0510 m
(b) m=− =− = −0.0204
do 2.50 m

ℎ𝑖 = 𝑚ℎ𝑜 = −0.0204 1.70 m = −0.0347 m

The Human Eye

The lens only contributes about 20-25% of the refraction, but its function is important.
 The Human Eye
NEARSIGHTEDNESS vs FASIGHTEDNESS

The lens creates an image of the distant object at The lens creates an image of the close object at the near
the far point of the nearsighted eye. point of the farsighted eye.
 The Dispersion of Light: Prisms and Rainbows
The net effect of a prism is to change the direction of a light ray. Light rays corresponding to different
colors bend by different amounts.
Summary
LAW OF REFLECTION SNELL’S LAW OF REFRACTION
𝒏𝟏 𝐬𝐢𝐧 𝜽𝟏 = 𝒏𝟐 𝐬𝐢𝐧 𝜽𝟐
The angle of incidence, 𝜽𝒊 equals the
angle of reflection, 𝜽𝒓 .
𝜽𝒊 = 𝜽 𝒓

Speed of light in vacuum 𝒄

INDEX OF REFRACTION 𝒏= =
Speed of light in the material 𝒗
 Summary
IMAGE FORMATION BY A CONVERGING LENS

IMAGE FORMATION BY A CONCAVE MIRROR

LOCATION of Object TYPE OF IMAGE SIZE ORIENTATION
LOCATION of Object TYPE OF IMAGE SIZE ORIENTATION Between Lens and F Virtual Larger Upright
Between mirror and F Virtual Larger Upright Between F and 2F Real Larger Inverted
Between C and F Real Larger Inverted Farther than 2F Real Smaller Inverted

IMAGE FORMATION BY A CONVEX MIRROR IMAGE FORMATION BY A DIVERGING LENS

The virtual image is diminished in size Image formed is always upright, virtual, diminished
and upright.
References
Cutnell, J. D. (2019). Physics: Biomedical Applications of Introductory
Physics. 11th ed. Wiley.

Young, H. D. and Freedman, R. A. (2016) University Physics with Modern

Physics, 14th ed. Pearson.

GE-PHY 101 Physics Group Lecture slides, Sir Oraa, Dr. Tibayan, Sir
Apuyan, Sir Abugao

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