17: Light Waves : Neet-xii-physics

Home Learn Fast select Course

Change Unit Change Subject Last Menu

NEET-XII-Physics

17: Light Waves

with Solutions - page 3

Note: Please signup/signin free to get personalized experience.

10 minutes can boost your percentage by 10%

Note: Please signup/signin free to get personalized experience.

Qstn #17
If Young’s double slit experiment is performed in water,
(a) the fringe width will decrease
(b) the fringe width will increase
(c) the fringe width will remain unchanged
(d) there will be no fringe
digAnsr: a
Ans : (a) the fringe width will decrease
As fringe width is proportional to the wavelength and wavelength of light is inversely proportional to the refractive index of the medium,
Here, `` {\lambda }_{{\rm M}}=\lambda /\eta ``
`` {\lambda }_{{\rm M}}=\,\mathrm{\,wavelength\,}\,\mathrm{\,in\,}\,\mathrm{\,medium\,}``
`` \lambda =\,\mathrm{\,wavelength\,}\,\mathrm{\,in\,}\,\mathrm{\,vacuum\,}``
`` \eta =\,\mathrm{\,refractive\,}\,\mathrm{\,index\,}\,\mathrm{\,of\,}\,\mathrm{\,medium\,}``
Hence, fringe width decreases when Young's double slit experiment is performed under water.
Page No 380:

#
Section : iii

Qstn #1
A light wave can travel
(a) in vacuum
(b) in vacuum only
(c) in a material medium
(d) in a material medium only
digAnsr: a,c
Ans : (a) in vacuum
(c) in a material medium
Light is an electromagnetic wave that can travel through vacuum or any optical medium.
Page No 380:

Qstn #2
Which of the following properties of light conclusively support the wave theory of light?
(a) Light obeys the laws of reflection.
(b) Speed of light in water is smaller than its speed in vacuum.
(c) Light shows interference.
(d) Light shows photoelectric effect.
digAnsr: b,c
Ans : (b) Speed of light in water is smaller than its speed in vacuum.
(c) Light shows interference.
Snell's Law, which states that the speed of light reduces on moving from a rarer to a denser medium, can be concluded from Huygens' wave theory and interference of light waves is based on the wave properties of light.
Page No 380:

Qstn #3
When light propagates in vacuum, there is an electric field as well as a magnetic field. These fields
(a) are constant in time
(b) have zero average value
(c) are perpendicular to the direction of propagation of light.
(d) are mutually perpendicular
digAnsr: b,c,d
Ans :
(b) have zero average value
(c) are perpendicular to the direction of propagation of light
(d) are mutually perpendicular
Light is an electromagnetic wave that propagates through its electric and magnetic field vectors, which are mutually perpendicular to each other, as well as to the direction of propagation of light. The average value of both the fields is zero.
Page No 380:

Qstn #4
Huygens’ principle of secondary wavelets may be used to
(a) find the velocity of light in vacuum
(b) explain the particle behaviour of light
(c) find the new position of a wavefront
(d) explain Snell’s Law
digAnsr: c,d
Ans : (c) find the new position of a wavefront
(d) explain Snell's Law
Huygen's wave theory explains the origin of points for the new wavefront proceeding successively. It also explains the variation in speed of light on moving from one medium to another, i.e. it proves Snell's Law.
Page No 380:

Qstn #5
Three observers A, B and C measure the speed of light coming from a source to be ν_A, ν_B and ν_C. A moves towards the source and C moves away from the source at the same speed. B remains stationary. The surrounding space is vacuum everywhere.
(a)
νA>νB>νC
(b)
νA<νB<νC
(c)
νA=νB=νC
(d)
νB=12νA+νC.
digAnsr: c,d
Ans :
(c) v_A₌v_B₌ v_C

(d) `` {\nu }_{B}=\frac{1}{2}\left({v}_{A}+{v}_{C}\right)``
Since the speed of light is a universal constant, v_A₌v_B₌ v_C= `` 3\times {10}^{8}`` m/s.
`` {\nu }_{B}=\frac{1}{2}\left({v}_{A}+{v}_{C}\right)``. This expression also implies that v_A₌v_B₌ v_C_.
1

Page No 380:

Qstn #6
Suppose the medium in the previous question is water. Select the correct option(s) from the list given in that question.
Ans : (a) v_A> v_B> v_C
(d) v_B= (v_A + v_C)/2
In any other medium, the speed of light is given by `` v=c/\eta ,\,\mathrm{\,where\,}\,\mathrm{\,\eta \,}\,\mathrm{\,is\,}\,\mathrm{\,the\,}\,\mathrm{\,refractive\,}\,\mathrm{\,index\,}\,\mathrm{\,of\,}\,\mathrm{\,the\,}\,\mathrm{\,medium\,}`` and according to Doppler effect, for an observer moving towards the source ,speed of light appears to be more than the other two cases. On the other hand, it will be least when the observer is moving away from the source.
Page No 380:

Qstn #7
Light waves travel in vacuum along the X-axis. Which of the following may represent the wave fronts?
(a) x = c
(b) y = c
(c) z = c
(d) x + y + z = c
digAnsr: a
Ans : (a) x = c
The wave is travelling along the X-axis. So, it'll have planar wavefront perpendicular to the X-axis.
Page No 380:

Qstn #8
If the source of light used in a Young’s double slit experiment is changed from red to violet,
(a) the fringes will become brighter
(b) consecutive fringes will come closer
(c) the intensity of minima will increase
(d) the central bright fringe will become a dark fringe
digAnsr: b
Ans : (b) consecutive fringes will come closer
Fringe width, `` \beta =\lambda D/d``.
Wavelength of red light is greater than wavelength of violet light; so, the fringe width will reduce.
Page No 380:

Qstn #9
A Young’s double slit experiment is performed with white light.
(a) The central fringe will be white.
(b) There will not be a completely dark fringe.
(c) The fringe next to the central will be red.
(d) The fringe next to the central will be violet.
digAnsr: a,b,d
Ans : (a) The central fringe will be white.
(b) There will not be a completely dark fringe.
(d) The fringe next to the central will be violet.
The superposition of all the colours at the central maxima gives the central band a white colour. As we go from the centre to corner, the fringe colour goes from violet to red. There will not be a completely dark fringe, as complete destructive interference does not take place.
Page No 380:

Qstn #10
Four light waves are represented by
(i)
y=a1 sin ωt(ii)
y=a2 sin ωt+ε(iii)
y=a1 sin 2ωt(iv)
y=a2 sin 2ωt+ε.
Interference fringes may be observed due to superposition of
(a) (i) and (ii)
(b) (i) and (iii)
(c) (ii) and (iv)
(d) (iii) and (iv)
digAnsr: a,i,ii,d,iii,iv
Ans : (a) (i) and (ii)
(d) (iii) and (iv).
The waves are travelling with the same frequencies and varying by constant phase difference.

#
Section : iv

Qstn #1
Find the range of frequency of light that is visible to an average human being
400 nm <λ<700 nm.
Ans : Given:
Range of wave length is
`` 400\,\mathrm{\,nm\,}<\lambda <700\,\mathrm{\,nm\,}``
We know that frequency is given by `` f=\frac{c}{\lambda }``,
`` \,\mathrm{\,where\,}\,\mathrm{\,c\,}=\,\mathrm{\,speed\,}\,\mathrm{\,of\,}\,\mathrm{\,light\,}=3\times {10}^{8}\,\mathrm{\,m\,}/\,\mathrm{\,s\,}``
f is the frequency
λ is the wavelength
We can write wavelength as:
`` \frac{1}{700\,\mathrm{\,nm\,}}<\frac{1}{\lambda }<\frac{1}{400\,\mathrm{\,nm\,}}``
`` \Rightarrow \frac{1}{7\times {10}^{-7}\,\mathrm{\,m\,}}<\frac{1}{\lambda }<\frac{1}{4\times {10}^{-7}\,\mathrm{\,m\,}}``
`` \frac{3\times {10}^{8}}{7\times {10}^{-7}}\,\mathrm{\,Hz\,}<\frac{c}{\lambda }<\frac{3\times {10}^{8}}{4\times {10}^{-7}}\,\mathrm{\,Hz\,}``
`` \Rightarrow 4.3\times {10}^{14}\,\mathrm{\,Hz\,}<\frac{c}{\lambda }<7.5\times {10}^{14}\,\mathrm{\,Hz\,}``
`` \Rightarrow 4.3\times {10}^{14}\,\mathrm{\,Hz\,}<f<7.5\times {10}^{14}\,\mathrm{\,Hz\,}``
Hence, frequency of the range of light that is visible to an average human being is `` 4.3\times {10}^{14}\,\mathrm{\,Hz\,}\,\mathrm{\,to\,}7.5\times {10}^{14}\,\mathrm{\,Hz\,}``.
Page No 380:

Qstn #2
The wavelength of sodium light in air is 589 nm.
Ans : Given:
Wavelength of sodium light in air, `` {\lambda }_{\,\mathrm{\,a\,}}=589\,\mathrm{\,nm\,}=589\times {10}^{-9}\,\mathrm{\,m\,}``
Refractive index of water, μ_w= 1⋅33
We know that `` f=\frac{c}{\lambda }``,
`` \,\mathrm{\,where\,}c=\,\mathrm{\,speed\,}\,\mathrm{\,of\,}\,\mathrm{\,light\,}=3\times {10}^{8}\,\mathrm{\,m\,}/\,\mathrm{\,s\,}``
f = frequency
λ = wavelength