Physics

Wave Optics and Diffraction

163 Questions

Wave optics explores light phenomena like interference and diffraction. This hub features problems on Young's double slit experiment, Fresnel biprism, and single slit diffraction patterns. These topics regularly appear in physics sections of competitive exams.

Young's double slitFresnel biprismSingle slit diffractionConstructive interferenceFringe width calculations

Wave Optics and Diffraction Questions

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

The ratio of intensities of two waves that produce interference pattern is 16:1, then the ratio of maximum and minimum intensities in the pattern is :

  1. 25:9

  2. 9:25

  3. 1: 4

  4. 4:1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the intensities of the two waves be $I _1$ and $I _2$.
Given :  $I _1:I _2 = 16:1$
Ratio of maximum and minimum intensities  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{I _1}  +\sqrt{I _2}}{\sqrt{I _1} - \sqrt{I _2}}\bigg)^2$
Or   $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{\frac{I _1}{I _2}}  +1}{\sqrt{\frac{I _1}{I _2}} - 1}\bigg)^2$

Or  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{16}  +1}{\sqrt{16} - 1}\bigg)^2 = \bigg(\dfrac{4+1}{4-1}\bigg)^2$
$\implies  \ $  $\dfrac{I _{max}}{I _{min}} = \dfrac{25}{9}$

Multiple choice physics superposition of waves-1: interference and beats interference of sound waves superposition and interference of sound waves properties of sound waves

Two waves having their intensities in the ratio 9:1 produce interference. In the interference pattern, the ratio of maximum to minimum intensity is equal to

  1. 2:1

  2. 9:1

  3. 3:1

  4. 4:1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the intensities of the two waves be $I _1$ and $I _2$.
Given :  $I _1:I _2 = 9:1$
Ratio of maximum and minimum intensities  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{I _1}  +\sqrt{I _2}}{\sqrt{I _1} - \sqrt{I _2}}\bigg)^2$
Or   $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{\frac{I _1}{I _2}}  +1}{\sqrt{\frac{I _1}{I _2}} - 1}\bigg)^2$

Or  $\dfrac{I _{max}}{I _{min}} = \bigg(\dfrac{\sqrt{9}  +1}{\sqrt{9} - 1}\bigg)^2 = \bigg(\dfrac{3+1}{3-1}\bigg)^2$
$\implies  \ $  $\dfrac{I _{max}}{I _{min}} = \dfrac{16}{4} = \dfrac{4}{1}$

Multiple choice physics wave optics polarization of light polarisation of light polarisation

A point source of monochromatic light is situated at the centre of a circle, what is the phase difference between the light waves passing through the end points of any diameter

  1. $\dfrac{\pi}{2}$
  2. $\pi$
  3. $\dfrac{3\pi}{2}$
  4. $zero$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A point source emits spherical waves. Any points at the same distance from the source, such as the endpoints of a diameter, lie on the same wavefront and thus have zero phase difference.

Multiple choice physics superposition of waves coherence young's double slit experiment interference

In a biprism experiment, the distance of 20 th bright bandfrom the center of the interference pattern is 8$\mathrm { mm }$ . The distance of 30th bright band from the center is

  1. $11.8\mathrm { mm }$
  2. 12$\mathrm { mm }$
  3. 14$\mathrm { mm }$
  4. 16$\mathrm { mm }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given

$\begin{array}{l} 20\beta =8mm \ \beta =\dfrac { 8 }{ { 20 } }  \ Now, \ 30th\, \, \max  ima=30\beta =\dfrac { { 30\times \beta  } }{ { 20 } } =12mm \ 30th\, \min  ima=\dfrac { { \left( { 2\left( { 30 } \right) -1 } \right)  } }{ 2 } \beta  \ =\dfrac { { 59 } }{ 2 } \beta  \ =\dfrac { { 59 } }{ 2 } \times \dfrac { 8 }{ { 20 } }  \ =11.8mm \ Hence,\, option\, A\, is\, the\, correct\, answer. \end{array}$

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Two coherent waves of light will not produce constructive interference if the phase difference between them is

  1. $0^0$
  2. $360^0$
  3. $720^0$
  4. $90^0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Constructive interference for coherent waves takes place when phase difference = $2n\pi$ where n is a integer

So the only case in the options when constructive interference will not take place is $90^\circ$

Answer. D

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Interference pattern can be produced by two identical sources. Here the identical sources mean that

  1. their size is same

  2. their wavelength is same

  3. the intensity of light emitted by them is same

  4. the emplitudes of light waves emitted by them are same
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For observing interference the term identical source means that their wavelength are the same ( i.e., they are coherent).

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Which of the following is not essential for two sources of light in Young's double slit experiment to produce a sustained interference?

  1. Equal wavelength

  2. Equal intensity

  3. Constant phase relationship

  4. Equal frequency
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For sustainable interference wavelength has to be same. So frequency has to be same too. Contact phase relation is also necessary to sustain the interference pattern else the pattern will keep changing so rapidly that we will not see any pattern.

Equal intensity is not a requirement to keep pattern sustained.

Answer. B) equal intensity

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Instead of using two slits, if we use two separate identical sodium lamps in Young's experiment, which of the following will occur?

  1. General illumination

  2. Widely separate interference

  3. Very bright maxima

  4. Very dark minima
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There will be general illumination as super imposing waves do not have constant phase difference.

Multiple choice physics superposition of waves coherence young's double slit experiment interference

In Young's double slit experiment, one slit is covered with red filter and another slit is covered by green filter, then interference pattern will be

  1. red

  2. green

  3. yellow

  4. invisible
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the red and green filters are used, the rays from slits will have wavelengths of red and green light.  The condition of mono chromatic sources will not be met. Hence, the fringe pattern will disappear.

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Two coherent sources of intensity ratio $\beta$ interfere. Then the value of $\displaystyle \left( {\frac{{{I _{\max }} - {I _{\min }}}}{{{I _{\max }} + {I _{\min }}}}} \right)$ is:

  1. $\dfrac{{1 + \beta }}{{\sqrt \beta }}$
  2. $\sqrt {\left( {\dfrac{{1 + \beta }}{\beta }} \right)} $
  3. $\dfrac{{1 + \beta }}{{2\sqrt \beta }}$
  4. $\dfrac{{2\sqrt \beta }}{{1 + \beta }}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{I _2}{I _1}=\beta$                        $\displaystyle \frac{I _{min}}{I _{max}}=\frac{\beta - 2 \sqrt{\beta}+1}{\beta + 2 \sqrt{\beta +1}}$
$\frac{A _2}{A _1} =\sqrt{\beta}$
$\displaystyle \frac{A _2 -A _1}{A _2 + A _1}=\frac{\sqrt{\beta}-1}{\sqrt{\beta}+1}$     $\displaystyle \frac{I _{max}- I _{min}}{I _{max}+ I _{min}}=\frac{(2)}{(2)} \left [ \frac{2 \sqrt{\beta}}{\beta +1}\right ]$

Multiple choice physics superposition of waves coherence young's double slit experiment interference

Interference fringes were produced in Young's double slit experiment using light of wavelength $5000\overset{o}{A}$. When a film of thickness $2.5\times 10^{-3}$cm was placed in front of one of the slits, the fringe pattern shifted by a distance equal to $20$ fringe-widths. The refractive index of the material of the film is?

  1. $1.25$
  2. $1.35$
  3. $1.4$
  4. $1.5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$n\lambda =\left( \mu -1 \right) t$\ $20\times 5\times  { 10 }^{ -7 }=\left( \mu -1 \right) 25\times { 10 }^{ -6 }$\ $\mu =1.4$

Multiple choice image formation by lens image formation by lenses ray optics and optical instruments optics physics

The distance between a point source of light and a screen which is $60$ $cm$ is increased to 180 cm. The intensity on the screen as compared with the original intensity will be : 

  1. $\cfrac { 1 } { 9 }$ times
  2. $\cfrac { 1 } {3 }$ time
  3. $3$ times
  4. $9$ times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Intensity is inversely proportional to the square of the distance from a point source (I proportional to 1/r^2). The distance increases from 60 cm to 180 cm, a factor of 3. Thus, the intensity changes by a factor of 1/(3^2) = 1/9.

Multiple choice evs light, shadows and images what makes things visible nature and sources of light light travels in straight line

In a YDSE with two identical slits, when the upper slit is covered with a thin, perfectly transparent sheet of mica, the intensity at the centre of screen reduces to $75\%$ of the initial value. Second minima is observed to be above this point and third maxima below it. Which of the following can be a possible value of phase difference caused by the mica sheet.

  1. $\dfrac{\pi}{3}$
  2. $\dfrac{13\pi}{3}$
  3. $\dfrac{17\pi}{3}$
  4. $\dfrac{11\pi}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Here when second order minica replaces bright spot change in path difference$3\pi $


Second order minica phase difference$\dfrac { \pi  }{ 2 } $

Phase difference lies between $3\pi\ to\ 4\pi $ i.e. $\dfrac{11\pi}{3}$

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

Huygens principle of secondary waves

  1. allow us to find the focal length of a thick convex lens.

  2. give us the magnifying power of the microscope.

  3. is a geometrical method to find, the position of a wave front.

  4. is used to determine the velocity of light.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Huygens's Principle states that every point on a wavefront is a source of secondary wavelets, which spread forward at the same speed.

Thus is enables to find the position of wavefront.

Multiple choice physics wave optics huygens wave theory and wavefront wave propagation (huygens' construction) theories on light wave behaviour

Huygen's concept of wavelets is useful in

  1. explaining polarisation

  2. determining focal length of lenses

  3. determining chromatic aberration

  4. geometrical reconstruction of a wavefront
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Huygens considered that light was propagated in longitudinal waves.
Huygen's concept explained the direction of propagation of light waves by geometrical reconstruction of wavefront.