Short Answer Questions
1. What is angle of deviation due to reflection?
The angle between the incident ray and deviated
ray of light is called angle of
2. Derive the relation between f and R for a spherical mirror.
Let C be the centre of curvature of the mirror. Consider a ray of light
parallel to the principal axis is incident on the mirror at M. It passes through
the principal focus F after reflection.
The line CM is the normal to the mirror at M.
Let i be the angle of incidence and
the same will be the angle of reflection.
If MP is the perpendicular from M on the principal axis, then The angles ∠MCP = i and. ∠MFP = 2i
right angle triangles ΔMCP and ΔMFP,
is focal length f and PC is the
radius of curvature R.
2f = R (or) f = R/2
is the relation between f and R.
3. What are the Cartesian sign conventions for a spherical mirror?
The incident light is taken as if it is travelling from left to right.
All the distances are measured from the
pole of the mirror.
The distances measured to the right of
pole along the principal axis are taken as positive.
The distances measured to the left of
pole along the principal axis are taken as negative.
Heights measured upwards perpendicular
to the principal axis are taken as positive.
Heights measured downwards
perpendicular to the principal axis are taken as negative.
4. What is optical path? Obtain the equation for optical path.
Optical path of a
medium is defined as the distance d’ light travels in vacuum in the
same time it travels a distance d in the medium.
❖ Consider a medium of refractive
index n and thickness d.
❖ Light travels with a speed v through the medium in a time t.
v = d/t
t = d/v
❖ In the same time, light can
cover a greater distance d' in vacuum as it travels with greater speed c in
c = d’ / t
t = d’ / c …………….(2)
equation (1) & (2)
d'/c = d/v
d’ = c/v × d
c/v = n; The optical path d’ = nd ……….(3)
❖ The value of n is always greater
than 1, for a medium. Thus, the optical path d' of the medium is always greater
5. State Snell's laws/law of refraction.
The incident ray, refracted ray and normal to the refracting surface are all coplanar.
The ratio of sine of angle of incident i
in the first medium to the sine of angle of refraction r in the second medium is equal to the ratio of refractive index n2 of the second medium to
the refractive index n1 of
the first medium.
i / sin r = n2 / n1
sin i = n2 sin r
6. What is angle of deviation due to refraction?
angle between the incident and deviated light is called angle of deviation.
❖ When light travels from rarer to denser medium it deviates towards normal.
= i − r
❖ When light travels from denser to rarer medium it deviated away from normal.
= r - i
7. What is principle of reversibility?
principle of reversibility states
that light will follow exactly the same path if its direction of travel is
reversed. This is true for both reflection and refraction.
8. What is relative refractive index?
❖ The term (n2/n1)
is called relative refractive index of second medium with respect to
the first medium which is given by
❖ Hence ratio of the refractive
index of 2nd medium to the refractive index of 1st medium
is called relative refractive index.
9. Obtain the equation for apparent depth.
❖ Let the light from the object O
at the bottom of the tank passes from water to air to reach our eyes.
= refractive index of water
= refractive index of air
i = angle of incidence in water
r = angle of refraction in air
Here n1 = n ; n2
= 1 & n1 > n2
❖ The lines NN' and OD are
parallel ie., ∠DIB = r
❖ Since diverging light entering
the eye is very narrow, i & r are very small.
∴ From Snell's law
sin i = n2 sin r ………..(1)
since i & r small angles
i ≈ tan i & sin r = tan r
tan i = n2 tan r
In triangles ΔDOB and ΔDIB,
The bottom appears to be elevated
d - d' = d[ l − 1/n ]……….(4)
10. Why do stars twinkle?
stars actually do not twinkle. They
appear twinkling because of the movement of the atmospheric layers with varying refractive indices which is clearly seen in the
11. What is critical angle and total internal reflection?
angle of incidence in the denser medium for which the angle of refraction is
90° (or) the refracted ray graces
the boundary between the two media is called critical angle ic.
any angle of incidence greater than the critical angle, the entire light is reflected back into the denser medium itself. This
phenomenon is called total internal
12. Obtain the equation for critical angle.
the definition of critical angle, using Snell's
law we can write
n1 sin ic
= n2 sin 90◦
n1 sin ic = n2
ic = n2 / n1 Here n1>
n1 = n (some medium) and
= 1 (air)
ic = 1/n
ic = sin-1 (1/n)
critical angle ic depends on the refractive index n of the medium.
13. Explain the reason for glittering of diamond.
Diamond appears dazzling because the total internal reflection of light happens
inside the diamond.
The refractive index of only diamond is about 2.417. It is much larger than that for ordinary glass which is
about only 1.5.
The critical angle of diamond is about 24.4°.
It is much less than that of glass.
A skilled diamond cutter makes use of this larger range of angle of incidence,
to ensure that light entering the diamond is total internally reflected from
the many cut faces before getting out.
This gives a sparkling effect for
14. What are mirage and looming?
refractive index of air increases with its density.
hot places, air near the ground is
hotter than air at a height. Hot air is less dense.
in still air the refractive index of air increases
of this, light from tall objects like a tree, try to pass through a medium
whose refractive index decreases towards
a ray of light successively deviates away from the normal at different layer of
air and undergoes total internal reflection when the angle of incidence
near the ground exceeds the critical
gives an illusion as if the light comes from somewhere below the ground. This
phenomenon is called mirage.
the cold places the refractive index
increases towards the ground because
the temperature of air close to the ground is lesser than the temperature above the surface of earth.
the density and refractive index of air
near the ground is greater than at a height.
an inverted image is formed little above the surface. This phenomenon is
is also called as superior mirage, towering and stooping.
15. Write a short notes on the prisms making use of total internal reflection.
Prisms can be designed to reflect light by 90°
or by 180° by making use of total
internal reflection as shown in Figure.
The critical angle ic for the material of the prism must be less
Here prism acts like a mirror of 100%
Prisms are also used to produce invert image of a object on the same side (or)
16. What is Snell’s window?
light entering the water from outside is seen from inside the water, the view
is restricted to a particular angle equal to the critical angle ic.
The restricted illuminated circular area is called Snell's window.
17. How does an endoscope work?
Endoscopes work on the phenomenon of total
internal reflection which has bundle of optical fibres is an instrument
used by doctors to see inside of a patient's body.
The optical fibres are inserted in to the body through mouth, nose or a special
hole made in the body.
Even operations could be carried out with the endoscope cable which has the necessary
instruments attached at their ends.
18. What are primary focus and secondary focus of a lens?
The primary focus F1 is
defined as a point where a point source kept produces a parallel emergent rays
to the principal axis after passing through lens.
ii) The secondary focus F2 is
defined as a point where all the parallel
rays travelling close to the principal axis converge to form an image on the principal axis after passing
19. What are the sign conventions followed for lenses?
The incident light is taken as it is travelling from left to right
All the distances are measured from the pole of the lens.
The distances measured to the right of pole along the principal axis are taken
The distances measured to the left of pole along the principal axis are taken
Heights measured upwards perpendicular to the principal axis are taken as
positive and downwards perpendicular to the principal axis are taken as
The sign of focal length is not decided on the direction of measurement of the
focal length from the pole of the lens.
focal length of the thin lens is taken as positive for a converging (convex)
lens and negative for a diverging (concave) lens.
20. Arrive at lens equation from lens maker’s formula.
to lens makers formula the difference in the reciprocal of object and image
distance is given by
the object is at infinity, the image is formed at the focus of the lens. ie: u = ∞; v = f
If n2 = n, n1 = 1 (air)
= (n-1) (1/R1 – 1/R2)
(1) and (2) we get equations
1/f = 1/v – 1/u
equation is known as lens equation.
21. Obtain the equation for lateral magnification for thin lens.
Consider an object OO’ of height h
placed on the principal axis with its height perpendicular to the principal
axis as shown in Figure.
The ray OP passing through the pole of the lens goes undeviated.
The inverted real image II’ formed has a height h’.
The lateral or transverse magnification m is defined as the ratio of the height
of the image to that of the object.
= II’ / 00’ ……………………(1)
the two similar triangles ∠POO’
and ∠PII’ , we can write
II’ / OO’ = P1/PO
-h’ / h = v / -u
this in the equation (1) for magnification
m = -h’ / h = v / -u
= h’ /
h = v/ u…………………(3)
The magnification is
negative for real image and positive for virtual image. In the
case of a concave lens, the magnification is always positive and less than one.
22. What is power of a lens?
Power of a lens is the measure of its
deviating ability on an incident light.
power of a lens is a measure of the
degree of convergence or divergence of light falling on it.
power of a lens P is defined as the reciprocal
of its focal length.
unit of power is dioptre (D) (or) m-1 power is positive for converging lens and negative for diverging lens.
23. Derive the equation for effective focal length for lenses in contact.
Consider two lenses (1) and (2) of focal length f1 and f2
are placed coaxially in contact with each other so that they have a common
For an object placed at O beyond the focus of the first lens (1) on the
principal axis, an image is formed by it at I'.
This image I' acts as an object for the second lens (2) and the final image is
formed at I as shown in Figure.
Let, PO be object distance u and PI’ be the image distance (v’) for
the first lens (1) and object distance for the second lens (2) and PI = v be
the image distance for the second lens (2).
the lens equation for first lens (1),
the lens equation for second lens (2)
the above two equations
the combination acts as a single lens of focal length F so that for an object
at the position O it forms the image at I then,
equations (3) and (4)
above equation can be extended for any number of lenses in contact as,
above equation can be written as power of the lenses as,
= P1 + P2 + P3 + P4 + ……... (7)
P is the net power of the lens combination of lenses in contact.
27. What is angle of minimum deviation?
angle of deviation decreases with increase in angle of incidence and reaches a
minimum value and then continues to increase.
minimum value of angle of deviation is called angle of minimum deviation D.
28. What is dispersion?
Dispersion is splitting of white
light into its constituent colours. This band of colours of light
is called its spectrum.
29. How are rainbows formed?
is an example of dispersion of sun light through droplets of water during rainy
When sunlight falls on the water drop suspended in air, it splits into its
constituent seven colours.
Thus, water drop suspended in air behaves as a glass prism.
Primary rainbow is formed when light entering the drop undergoes one total
internal reflection inside the drop before coming out from the drop.
The angle of view for violet to red
in primary rainbow is 40° to 42°.
A secondary rainbow appears outside of a primary rainbow and develops when
light entering a raindrop undergoes two total internal reflections.
The angle of view for red to violet
in a secondary rainbow is 52° to 54°.
30. What is Rayleigh’s scattering?
the scattering of light is by atoms and molecules which have size a very much
less than that of the wave length λ of light (a << λ ), then the scattering is called Rayleigh's scattering.
31. Why does sky appear blue?
to Rayleigh scattering law violet colour which has the shortest wavelength gets
more scattered than the other colours. The next scattered colour is blue. As our eyes are more sensitive to blue colour than violet colour, the sky appears
blue during day time.
32. What is the reason for reddish appearance of sky during sunset and sunrise?
sunrise and sunset, the light from sun travels a greater distance through the
atmosphere. Hence, According to Rayleigh scattering law the blue light which
has shorter wavelength is scattered away and the less-scattered red light of
longer wavelength manages to reach our eyes. So the sky appear reddish during
sunset and sunrise.
33. Why do clouds appear white?
If light is scattered by large particles like dust and water droplets present in the atmosphere which have size a greater than the wavelength λ of light, a >> λ, the intensity of scattering is equal for all the colours. It is happening in clouds which contains large amount of dust and water droplets. Thus, in clouds all the colours get equally scattered irrespective of wavelength. This is the reason for the whitish appearance of cloud.