Tag: difference between interference and diffraction

Questions Related to difference between interference and diffraction

Two wave-fronts are emitted from coherent sources of path difference between them is $2.1$ micron. Phase difference between the wave-fronts at that point is $7.692\ \pi$. Wavelength of light emitted by sources will be :

physics superposition of waves difference between interference and diffraction explaining wave phenomena diffraction

  1. $5386\mathring{A}$

  2. $5400\mathring{A}$

  3. $5460\mathring{A}$

  4. $5892\mathring{A}$

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Correct Option: C
Explanation:
Given:
$\Delta x=2.1 \times 10^{-6}\\\Delta \phi=7.6922$

$\Phi =\dfrac{2\pi \Delta x}{\lambda}$

$\lambda=\dfrac{2\pi\times 2.1\times 10^{-6}}{7.692\pi}$

$\lambda=5460\times 10^{-10}m$

A screen is at a distance of $1\ m$ away from the aperture. If light of wavelength $500\ nm$ falls on an aperture, then area of first HPZ and radius of third HPZ are :

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. $1.57\ mm^2, 1.22\ mm$

  2. $1.22\ mm^2, 1.57\ mm$

  3. $1.65\ mm^2, 2.79\ mm$

  4. $2.63\ mm^2, 0.22\ mm$

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Correct Option: A

The sodium yellow doublet has wavelengths $5890\mathring{A}$ and $'\lambda' \mathring{A}$ and resolving power of a grating to resolve these lines is $982$, then value of $\lambda$ is :

physics superposition of waves difference between interference and diffraction explaining wave phenomena diffraction

  1. $5896\mathring{A}$

  2. $5880\mathring{A}$

  3. $5869\mathring{A}$

  4. $5876\mathring{A}$

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Correct Option: A

The phenomenon of diffraction can be treated as interference phenomenon if the number of coherent sources is 

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. one

  2. two

  3. zero

  4. infinity

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Correct Option: D
Explanation:

The single slit diffraction pattern acts as an envelope for the multiple slit interference patterns.

Diffraction on a single slit is equivalent to interference of light from infinite number of coherent sources contained in slit.

In Fresnel's biprism expt., a mica sheet of refractive index 1.5 and thickness 6 $\times$ 10$^{-6}$m is placed in the path of one of interfering beams as a result of which the central fringe gets shifted through 5 fringe widths. The wavelength of light used is

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. 6000 $\overset{o}{A}$

  2. 8000 $\overset{o}{A}$

  3. 4000 $\overset{o}{A}$

  4. 2000 $\overset{o}{A}$

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Correct Option: A
Explanation:

Where n is equivalent number of fringe by which the centre fringe is shifted due to mica sheet
$\displaystyle\lambda = \frac{(\mu - 1)t}{n} = \frac{(1.5 - 1) 6 \times 10^{-6}}{5} = 6 \times 10^{-7} m = 6000 \overset{o}{A}$

An aperture of size a is illuminated by a parallel beam of light of wavelength $\lambda$. The distance at which ray optics has a good approximation is

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. $\dfrac {a^{2}}{\lambda}$

  2. $\dfrac {\lambda}{a^{2}}$

  3. $\dfrac {\lambda}{a}$

  4. $\dfrac {\lambda^{2}}{a}$

  5. $a^{2}\lambda$

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Correct Option: A
Explanation:

An aperture of size a is illuminated by a parallel beam of light of wavelength $\lambda$. The distance at which ray optics has a good approximation is $\dfrac {a^{2}}{\lambda}$. This is the Fresnel distance.

Diffraction gratings provide much brighter interference pattern since more light passes through them compared with double slits.

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. True

  2. False

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Correct Option: A
Explanation:

The statement is true.

That is diffraction gratings provide much brighter interference pattern since more light passes through them compared with double slits.
One difference between the interference of many slits (diffraction grating) and double-slit (Young's Experiment) is that a diffraction grating makes a number of principle maxima along with lower intensity maxima in between.  The principal maxima occur on both sides of the central maximum for which a formula similar to Young's formula holds true.

In biprism experiment, the distance of 20th bright band from the centre of the interference pattern is 8 mm. The distance of the 30th bright band is

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. 4 mm

  2. 8 mm

  3. 12 mm

  4. 16 mm

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Correct Option: C
Explanation:

Given

$20\cfrac { \lambda D }{ d } =8\ =\cfrac { \lambda D }{ d } =\cfrac { 8 }{ 20 } \ \therefore  { 30 }^{ th }$ bright,
$=30\times \cfrac { \lambda D }{ d } \ =30\times \cfrac { 8 }{ 20 } \quad =12mm$

In a biprism experiment, the fringe width obtained on the screen is $6\ mm$ from the slits which are $1.5\ m$ away from each other. Keeping the setting unchanged if the eye-piece is moved $20\ cm$ towards the biprism, find the change in fringe width.

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. $0.90\ mm$

  2. $0.86\ mm$

  3. $0.80\ mm$

  4. $0.53\ mm$

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Correct Option: A

In a Fresnel's bi-prism experiment, the fringe of width $0.05mm$ is observed on a screen at a distance of $1.5m$ from the source . When a convex lens is placed between the source and the screen, for two positions of the lens image of interfering sources are produced on the screen. The separation between the two images being $0.04$ and $0.01mm$, respectively. The wavelength of light used is

physics wave optics difference between interference and diffraction explaining wave phenomena diffraction

  1. $6.67nm$

  2. $0.667nm$

  3. $667nm$

  4. $667A^o$

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Correct Option: B
Explanation:

Distance between slits, $d=\sqrt{d _{1}d _{2}}=0..02mm$

Fringe width, $\beta=\dfrac{D\lambda}{d}$
hence $\lambda=\dfrac{\beta d}{D}=0.667nm$