Optics

CHAPTER 8:RAY OPTICS (9%)

REFLECTION OF LIGHT BY SPHERICAL MIRRORS

Concave (converging) mirror

Convex (diverging) mirror

Paraxial rays: are the rays parallel to principal axis which makes angle of incidence in
the mirror close to zero (< 10 degree).

If the rays are not paraxial, the image will not be sharp. This defect in image
formation is known as spherical aberration. This defect is due to the spherical nature
of the surface.
Spherical aberration is the distortion of an image produced by a concave mirror that is
spherical rather than parabolic. In smaller mirrors spherical aberration is less noticeable
than in larger mirrors.

Concave mirrors are used as reflector in search lights, head light of motor vehicles, in
telescopes, in solar cookers, and as shaving mirrors, dentist mirror.

USES OF CONCAVE MIRRORS

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Open Ended

Why convex mirror is used as a traffic mirror?

USES OF CONVEX MIRRORS

Convex mirrors are used as reflector in street lamps and as rear view mirrors in motor vehicles
(because of their large field of view).

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Lateral magnification of a mirror is the ratio of the height of the image to the height of the object,
which is denoted by m.

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-Interactives/Reflection-and-Mirrors/Optics-
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The Mirror Equation

Finding the Details of the Image from 1/v versus 1/u Graph

Concave mirror:
Since the graph (line) does not
occupy the first quadrant, the
combination of virtual object- virtual
image (u=+,v=+) is not possible for
concave mirror.

Convex mirror:
Since the graph (line) does not
occupy the third quadrant, the
combination of real object- real
image (u= -,v= -) is not possible for
convex mirror.

Concave mirror

Convex mirror

1. A dentist uses a concave mirror to examine a tooth that is 1.00 cm in front of the
mirror. The image of the tooth forms 10.0 cm behind the mirror.
a) What is the mirror’s radius of curvature? b) What is the magnification of the
image?
2.Why is shaving with a concave mirror preferable than shaving with a plane
mirror?
3.Two concave mirrors have the same focal length but the aperture of one is larger
than that of
4.the other. Which mirror forms the sharper image and why?

4.How will you distinguish between a plane, a concave and a convex mirror without
touching its surface?
5.A man stands in front of a unique-shaped mirror. He discovers that his image has
a small head, a fat body, and normal-sized legs. What do you think of the three
components of the mirror's shapes?

REFRACTION AT SPHERICAL SURFACES

Convex (converging) lens

Concave (diverging) lens

The linear magnification (transverse magnification) of a lens is the ratio of the height of the image to the
height of the object.

REFRACTION BY SPHERICAL LENSES

The Lens Equation (derivation is in the syllabus)

Magnification equation of lens

Power of a Lens
The ability of a lens to bend (converge or diverge) the rays of light incident on it is called the power of
the lens. The power of a lens is measured by the reciprocal of its focal length (in metres).

For a converging lens the power is positive, and for a diverging lens the power is negative because
converging lenses have positive focal length and diverging lenses have negative focal length.

LENS MAKER’S FORMULA

Combination of Thin Lenses in Contact

When two lenses are kept in contact, then the equivalent focal length is

If there are more than 2 lenses in contact, we apply the same formula to find the equivalent focal length.

1.A convex lens forms a real image of a point object placed on its principal axis. If the upper half
of the lens is painted black, the image will not be shifted. Why?

1.A convex lens forms a real image of an object for its two different positions on a screen. If
height of the image in both the cases be 8 cm and 2 cm, what is the height of the object?

1.How focal length of the lens immersed in liquid changes with the following conditions:

1. a) If the refractive index of liquid is equal to refractive index of lens,
2. b) If the refractive index of liquid is less than refractive index of lens and
3. c) If the refractive index of liquid is greater than the refractive index of lens.

2.An object placed 4 cm in front of a converging lens produces a real image 12 cm from the lens.
What is the magnification of the image? What is the focal length of the lens? Draw the ray
diagram to show the formation of the image based on the above conditions..

1.A convex lens of focal length 0.10 m is used to form a magnified image of an object of height
5 mm placed at a distance of 0.08 m from the lens. Find the position, nature and size of the
image.

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Questions

1. A glass lens of refractive index 1.5 is placed in a trough of liquid. What
must be the refractive index of the liquid in order to make the lens
disappear?

2. A converging lens of refractive index 1.5 is kept in a liquid medium
having same refractive index. What would be the focal length of the lens
in this medium?

3. How does the power of a convex lens vary, if the incident red light is replaced by violet light?

4. Two thin lenses of power + 4D and – 2D are in contact. What is the focal
length and nature of the combination?

5. A converging lens is kept coaxially in contact with a diverging lens — both
the lenses being of equal focal lengths. What is the focal length of the
combination?

6. When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed
imply a decrease in the energy carried by the light wave? Justify your answer.

7.A biconvex lens made of a transparent material of refractive index 1.25 is
immersed in water of refractive index 1.33. Will the lens behave as a
converging or a diverging lens? Give reason.

8. What is the focal length of a convex lens of focal length 30 cm in contact with
a concave lens of focal length 20 cm? Is the system a converging or diverging
lens? What is the power of the combination?

9. How will the position and intensity of the image be affected if the lower half
of the mirror’s reflecting surface is painted black?

10. Which mirror is used as side view mirrors in vehicles and why? State
the nature of the image.

11.The image obtained with a convex lens is erect and its length is four times the length of the object.
If the focal length of the lens is 20 cm, calculate the object and image distances.
12. A convex lens is used to obtain a magnified image of an object on a
screen. The object is at a distance of 10 m from the lens. If the magnification
is 19, find the focal length of the lens.

The human eye is just like a camera, its lens system forms an image on a light-
sensitive screen called the retina. Our eye has the ability to see the near and distant
objects due to the flexible capability of the crystalline lens behind the cornea, the
crystalline lens is composed of fibrous jelly-like material called ciliary muscles. When
we see the distant object these muscles relax resulting the eye lens becomes thin,
means the radius of curvature of the eye lens becomes larger. The larger radius of the
curvature results in a larger focal length of the lens focusing the image of the object at
the retina.

When we see the nearer object the ciliary muscle contracts reducing the radius of
the curvature of lens thereby decreases the focal length of the lens and thus
focusing the image of the object at the retina, thus a healthy eye is capable to see
near and far objects. The property of the eyes of adjusting its focal length to see the
nearby and distant object is known as accommodation of the eye.

Accommodation of the eyes

Myopia

Myopia is also called nearsightedness, it is the defect of the human eye due to
which we can’t see the distant object, we can see the nearby object but after a
certain distance, we can not see the objects and the so formed image looks blurred.
Generally, myopia is occurred during childhood due to the growth of eyes within
the age of 20 years but it may occur to anybody due to our habit of seeing television
by sitting near about it, excess reading or improper way of reading, diabetes, etc.

Myopia is caused by bulging cornea due to which radius of the curvature of the
whole of the eye decreases and the focal length of the eye is decreased, the eye
becomes unable to focus the image of distant objects at the retina and thus image is
formed near the eye lens, it is that’s why this defect of eye is called nearsightedness
or myopia, as a result of this defect of eye( myopia) the far objects look blurred. The
maximum distance at which an object could be seen by a myopic eye is known as
its far point beyond this far point image is formed near the eye lens instead of at
retina.

Treatment of myopic eye- The myopic eye is treated by applying a concave lens
of a particular focal length, depends on the far point, as an example shown below.

Example- If the far point of an eye of a person is 100 cm, then find the type of lens
and its focal length used for the treatment of clearing his vision.

Answer. The far point of the person’s eye 100 cm reveals that he can not see the
things beyond 100 cm, so he is needed a diverging lens(concave ) of focal length f
so that the image could be formed at the far point of the eye as seen in the
following diagram.

Its meaning is the lens required for such an eye
is –1 D , after applying this lens the person could
see beyond the distance of 100 cm.

f = ?, v = –100 cm, u =

f = –100 cm
Hence the power of the lens
will be

Power of the lens = –1 D

Hypermetropia/ farsightedness

This is the defect of an eye due to which a person is capable to see the
distant objects but is unable to see the nearby object. Hypermetropia
occurred when the ciliary muscles of the lens is unable to contract and
thus focal length of the eye lens increase that image of the nearby
objects is formed beyond the retina, that is far from the eye lens that’s
why hypermetropia is also called farsightedness.

Example- An eye's near point is 50 cm, find the treatment of this eye to correct vision.Answer. Near point 50 cm means that the eye is unable to see the object nearer to 50 cm, thus
the given eye
is suffering from hypermetropia.To overcome this problem a convex lens of focal length f
must be used so that
if now the distance is 25 from the lens then the image could be formed at the near point of the
eye.
u =– 25 cm

v = – 50 cm

Power of the lens = +2D,
The focal length of the convex lens is 50 cm
50 cm = 0.5 m

A person with myopic vision see objects only up to a distance of 0.25m. To be

able to read a book placed at the distance of 0.50m from the eyes, the

spectacles needed by this person have power of

A. - 1.0D

B. - 1.5D

C. - 2.0D

D. + 2.0D

Make a diagram to show how hypermetropia is corrected. The near point of hypermetropic eye is 1 m.
What is the power of lens required to correct this defect? Assume that the near point of the normal
eye is 25 cm.

A convex lens converges the incoming light such that the
image is formed on the retina.
An object at 25 cm forms an image at the near point of the
hypermetropic eye. Here, near point is 1 m.
Given,
Object distance, u=−25 cm

Image distance, v=−100 cm

From lens formula,

Focal length, f=100/3 cm =1/3 m
Power, P=1/f ​=3 D

13. Calculate the distance of an object of height ‘h’ from a concave mirror of
radius of curvature 20 cm, so as to obtain a real image of magnification 2.
Find the location of image also.

14. Using mirror formula, explain why does a convex mirror always produce a virtual image.

15. Using graphs show which object-image combination is impossible to achieve for convex and concave mirrors
individually?

Using a mirror, you want to focus an upright image of double the size of the
object. If your mirror has a focal length of 20 𝑐𝑚, at what distance will you place
your object in front of the mirror for this situation? [2]

A concave mirror produces a real image twice the size of the object
when placed at a distance of 22.5 cm from it. Where should be object be
placed so that the size of the image becomes three times that of the
object?

A man stands in front of a mirror of special shape. He finds that his image has a very
small head, a fat body and legs of normal size. What can we say about the nature of
the mirrors depending on their reflections? [3]

From the ray diagram show, calculate the focal length of the concave lens. [2]

A candle is burning at a distance on one side of a glass box. A same size image of the
candle is formed on a screen at 20 cm on the other side of the box. What optical device is
there in the box? What is its power? [2]

A convex lens of focal length 13 m forms a real, inverted image twice in size of the
object. The distance of the object from the lens is …………….

Karma combined a convex lens of focal length 20 cm with a concave lens of focal
length 15 cm. Then he tried to focus the image of a distant tree on a white screen
through the combined lenses. Will he be able to observe the image on the screen?
Give a reason. [2]

Both convex and concave mirrors can be used for shaving. Which mirror is preferred?
Explain. [2]

A plane wave passes through a convex lens. The geometrical shape of the wavefront that
emerges is
A. Diverging spherical.
B. cylindrical.
C. converging spherical.
D. plane.

For a spherical mirror, which is the correct graph of 1/𝑣 versus 1/𝑢 among the four graphs
shown below?

The table below shows the functional applications exhibited by mirror 𝑋 and mirror 𝑌.
Use the information given below to analyze the nature of mirror in relation to its usage.

Mirror 𝑿
Mirror 𝒀

Used by dentist and solar furnace
Images formed can be diminished as
well as enlarged

Used in rear view mirror
Virtual, erect, and diminished images
are always formed

A. Both the mirrors are convex
B. Both the mirrors are concave
C. 𝑋 is concave and 𝑌 is convex
D. 𝑋 is convex and 𝑌 is concave

A concave mirror of focal length 𝑓 produces an image 𝑛 times the size of the object. If
the image is real then the distance of the object is:
A. (𝑛−1)𝑓
B. (𝑛+1)𝑓
C. (𝑛+1/𝑛)𝑓
D. (𝑛−1/𝑛)𝑓

According to Cartesian sign convention, the focal length of concave mirror is --------------
------------------ and focal length of convex mirror is -------------------------------------- in
sign.

A double convex lens has 10 cm and 15 cm as radii of curvature. The image of an
object placed 30 cm from the lens, is formed at 20 cm from the lens on the other
side. Find the focal length and refractive index of material of the lens. [2]

Using a mirror, you want to focus an upright image of double the size of the object on the
screen. If your mirror has a focal length of 20 𝑐𝑚, at what distance will you place your
object in front of the mirror for this situation? [2]

During one of the physics practical of lenses, teacher showed the experimental set-up as
shown in the figure below. Using the figure below, answer the following questions that
follows; [2]

What is the aim of the above experiment?
Using the above symbols, proof that 𝑓=𝑓1𝑓2/(𝑓1+𝑓2), where symbols have their
usual meaning.

List down the materials required to carry out this experiment.

Mr. Penjor wanted to make a pair of spectacles of power +5D for his daughter
having eye sight problem. He had a convex lens of focal length 25 cm. Which of
the following lenses did he use to combine with his lens?

A. Convex lens of focal length 25 cm
B. Concave lens of focal length 25 cm
C. Convex lens of focal length 100 cm
D. Concave lens of focal length 100 cm

i.
In case of a concave mirror, the image of an object is

A. real, erect and diminished when the object lies beyond the centre of curvature.
B. real, inverted and of the same size as the object when it lies between centre of

curvature and focus.

C. real, inverted and diminished when object lies beyond the centre of curvature.
D. virtual, erect and diminished when object lies beyond the centre of curvature.

Lens X

Lens Y

➔ Used in flashlight
➔ Forms virtual and diminished image

➔ Used as magnifying glass and Microscope
➔ Forms real or virtual image based on the position
of the object.

•The table below shows the functional applications of lens X and Y. Use the
information from the table and identify the nature of the lens in relation to its usage in
spy holes in doors.

•Both the lenses are concave
•X is concave and Y is convex
•Both the lenses are convex
•X is convex and Y is concave

i. _______________mirror and ________________ lens produce virtual and

magnified image.

a) During physics practical class, you are asked to place a convex lens and concave

lens in contact to obtain the combined focal length experimentally. The focal
lengths of convex lens and concave lens were 20 cm and 30 cm respectively.
Determine the combined focal length theoretically to compare your practical
result.

a) Why are mirrors used in search light is parabolic and not concave spherical?

[1]

(i) .................mirror always gives diminished, virtual and erect image of all

real objects and its magnification is always ............. than unity.

i) Tashi combined a convex lens of focal length 20 cm with a concave lens of focal length

15 cm. Then he tried to focus the image of a distance tree on a white screen through the

combined lenses. Will he be able to observe the image on the screen? Give a reason.

[2]

i. If the magnification is calculated to be 0.5 in a particular situation, what does that tell

you about the image?

A. It is 0.5 meters tall.

B. It is bigger by 0.5

C. It is twice the size of the image.

D. It is half the size of the object.

i. A _____________ image is not formed by the actual intersection of light rays

while _____________ image is formed by the actual intersection of light rays.

i. A point source of light is placed at a distance of 2f from a converging lens of focal

length f. The intensity of light on the other side of the lens is maximum at a distance

A. f
B. 2f
C. more than 2f
D. between f and 2f

i. Image formed by concave mirror can be
A. real
B. inverted
C. diminished
D. all of the above

Analyse the following observation table showing variation of image - distance (v) with object -
distance (u) in case of a convex lens and answer the questions that follow without doing any
calculations:
(a) what is the focal length of the convex lens? Give reason to justify your answer.
(b) Write serial number of the observation which is not correct. On what basis have you arrived
at this conclusion?
(c) Select an appropriate scale and draw a ray diagram for the observation at S.No. 2. Also
calculate the approximate value of magnification.

(d) A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what
distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image.
If the candle is moved closer to the mirror, how would the screen have to be moved?

[3]

Object distance, u=−27cm

Radius of curvature of the concave mirror, R=−36cm

focal length of mirror f=R/2=−18cm

The image distance can be obtained using the mirror formula,

1/V+1/U=1/f
From above equation, v=−54cm.

Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image. The
magnification of the image is given as,

m=hi/ho

∴h′=−5cm