Maxima & Minima in YDSE

Q.

In Young's double-slit experiment , the intensity of light at a point on the screen where the path difference is $\lambda$ is K units. What is the intensity of light at a point where the path difference is $\lambda /3;$ $\lambda$ being the wavelength of light used?

1. K/4
   

2. K/2
   

3. K/3
   

4. K

Q. Youngs double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly

1. 1.59
2. 1.69
3. 1.78
4. 1.25

Q.

In young's double slit experiment, the two slits act as coherent sources of equal amplitude A and of wavelength $\lambda .$ In another experiment with the same set up, the two slits are sources of equal amplitude A and wavelength $\lambda$ but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case of that in the second case is

1. $\sqrt{2}:1$

2. 1:1
   

3. 1:2
   

4. 2:1
   

Q.

In Young’s double-slit experiment, the width of one of the slits is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

1. $4:1$

2. $3:1$

3. $2:1$

4. $1:4$

Q.

Two coherent light sources having intensity $I_1$ and $I_2$. If the ratio of $I_{max}:I_{min}$ is $25:9$. Find $\frac{I_1}{I_2}$​​?

1. $\frac{4}{1}$

2. $\frac{16}{1}$

3. $\frac{16}{9}$

4. $\frac{25}{9}$

Q. Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is $25:1$. The intensities of the sources will be in the ratio

1. $9:5$
2. $5:9$
3. $25:1$
4. $9:4$

Q.

Light of wavelengths $\lambda$ is incident on a slit of width d. The resulting diffraction pattern is observed on a screen at a distance D. The linear width of the principal maximum is equal to the width of the slit if D equals

1. $\frac{2\lambda }{d}$
   

2. $\frac{d}{\lambda }$
   

3. $\frac{d^2}{2\lambda }$
   

4. $\frac{2{\lambda }^2}{d}$

Q. Two slits separated by a distance of $1mm$ are illuminated with red light of wavelength $6.5\times {10}^{-7}m$. The interference fringes are observed on a screen placed $1m$ from the slits. The distance between the third dark fringe and the fifth bright fringe is equal to

1. $1.625mm$
2. $3.25mm$
3. $0.65mm$
4. $0.975mm$

Q. If the ratio of intensity of two coherent sources is $4,$ then the visibility $\frac{I_{max}-I_{min}}{I_{max}+I_{min}}$ of the fringes is

1. $4$
2. $\frac{4}{5}$
3. $\frac{3}{5}$
4. $9$

Q. (a) In Young's double slit experiment, describe briefly how bright and dark fringes are obtained on the screen kept in front of a double slit. Hence obtain the expression for the fringe width.

(b) The ratio of the intensities at minima to the maxima in the Young's double slit experiment is 9:25. Find the ratio of the widths of the two slits.

Q. In YDSE distance between slits and screen is $1.5\text{m}$. When light of wavelength $500\text{nm}$ is used then $2^{nd}$ bright fringe is obtained on screen at a distance of $10\text{mm}$ from central bright fringe. What will be shift in position of $2^{nd}$ bright fringe, if light of wavelength $550\text{nm}$ is used ?

1. $2\text{mm}$
2. $1\text{mm}$
3. $1.5\text{mm}$
4. $1.1\text{mm}$

Q. In a Youngs double slit experiment, the fringe width is found to be $0.4mm$. What will be the new fringe width, if the whole apparatus is immersed in a water of refractive index 4/3 without disturbing the geometrical arrangement?

1. 0.30 $mm$
2. 0.40 $mm$
3. 0.53 $mm$
4. 450 $mm$

Q. In Young's double slit experiment, the fringes are formed at a distance of $1\text{m}$ from double slit of separation $0.12\text{mm}$. Given $\lambda =6000\stackrel{\circ }{A}$. Then the distances of 3rd dark band from the centre of the screen and 3rd bright band from the centre of the screen will be respectively

1. $1.25\text{cm},1.5\text{cm}$
2. $2.25\text{cm},2.5\text{cm}$
3. $3.25\text{cm},3.5\text{cm}$
4. $0.25\text{cm},0.5\text{cm}$

Q.

Consider the situation shown in figure (17-E6). The two slits $S_1$ and $S_2$ placed symmetrically around the central line are illuminated by a monochromatic light of wavelength $\lambda$ the separation between the slits is d. The light transmitted by the slits falls on a screen ${\sum }_1$ placed at a distance D from the slits. The slit$S_3$ is at the central line and the slit $S_4$ is at a distane z rom $S_3$ Another screen ${\sum }_2$ is palced a further distance D away from ${\sum }_1$ find the ration of thmaximum to minimum intensity obsered on ${\sum }_2$ if z is equal to
(a) $z=\frac{\lambda D}{2d}$
(b) $\frac{\lambda }{d},$
(c) $\frac{\lambda D}{4d}.$

Q.

The distance between the interatomic lattice plane is $10Ă$. The maximum wavelength of X-rays which are diffracted by the crystal will be

1. $10Ă$

2. $20Ă$

3. $30Ă$

4. $40Ă$

Q.

Two coherent light sources of intensity ratio n are employed in an inteference experiment. The ratio of the intensities of the maxima and minima in the inteference pattern is

1. ${\left(\frac{n+1}{n-1}\right)}^2$
   

2. $\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)$
   

3. ${\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)}^2$

4. $\left(\frac{n+1}{n-1}\right)$
   

Q.

In an interference experiment, the spacing between successive maxima or minima is

1. $\frac{\mu d}{D}$

2. $\frac{\lambda D}{d}$

3. $\frac{dD}{\lambda \mu }$

4. $\frac{\mu \lambda }{4D}$

Q.

In Young's double slit experiment using two identical slits, the intensity of the maximum at the centre of the screen is I. What will be the intensity at the centre of the screen if one of the slits is closed?

1. None of these

2. I
   

3. $\frac{I}{2}$
   

4. $\frac{I}{4}$
   

Q. The figure below shows the path of white light’s rays which leave in phase from two small sources $S_1$ and $S_2$ and travel to a point X on a screen. The path difference is $S_{2}X-S_{1}X=8.7\times {10}^{-7}m$. What wavelength of light gives complete destructive interference at X?

1. $4.0\times {10}^{-7}m$
2. $4.4\times {10}^{-7}m$
3. $6.6\times {10}^{-7}m$
4. $5.8\times {10}^{-7}m$

Q.

If the fringe width is $0.4mm$, the distance between the fifth bright and third dark band on the same side is

1. $1mm$

2. $2mm$

3. $3mm$

4. $4mm$

Q. When monochromatic light travels from one medium to another, its wavelength changes but frequency remains the same. Explain.

Q. In YDSE apparatus shown in figure wavelength of light used is $\lambda$. The screen is moved away from the source with a constant speed $v$. Initial distance between screen and plane of slits was $D$ and at point $P$ on screen, $n^{th}$ order bright fringe is observed.

As the screen moves away value of $n$ will

1. increase
2. decrease
3. first increase then decrease
4. remain constant

Q.

In Young's double-slit experiment , the intensity of light at a point on the screen where the path difference is $\lambda$ is K units. What is the intensity of light at a point where the path difference is $\lambda /3;$ $\lambda$ being the wavelength of light used?

1. K/4

2. K/3

3. K/2

4. K

Q. In YDSE if the source consists of two wave lengths λ1=4000a° and λ2=4002A° . Find the dis†an ce from centre where fringes disappear if d=1cm;D=1m

Q. The intensity of central maximum in the interference pattern obtained by two coherent sources of wavelength $\lambda$ and amplitude a is I. In other experiment, the intensity of central maximum in the interference pattern obtained by two non – coherent sources of wavelength $\lambda$ and amplitude a is I' The value of I' will be

1. I
2. $\frac{I}{2}$
3. $\frac{I}{3}$
4. $\frac{I}{4}$

Q. In the figure shown, a parallel beam of light is incident on the plane of the slits of Young's double slit experiment. Light incident on the slit $S_1$ passes through a medium of variable refractive index $\mu =1+ax$ (where ${}^{\prime }{x}^{\prime }$ is the distance from the plane of slits as shown), up to a distance ‘𝑙’ before falling on $S_1$. Rest of the space is filled with air. If at ${}^{\prime }{O}^{\prime }$ a minima is formed , then the minimum value of the positive constant a (in terms of $l$ and wave length ${}^{\prime }{\lambda }^{\prime }$ in air) is

1. $\frac{l^2}{\lambda }$
2. $\frac{\lambda }{l}$
3. None of these
4. $\frac{\lambda }{l^2}$

Q. In Young's double slit experiment, if the separation between slit plane and screen is doubled and the wavelength of coherent light used in two slits is halved, then fringe width -

1. Becomes half
2. Becomes four times
3. Becomes one-fourth
4. Remains unchanged

Q. The width of one of the two slits in a Young's double slit experiment is double of the other slit. Assuming that the amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

Q. In a YDSE experiment shown, monochromatic light of wavelength $\lambda$ is used. Given $D=2m$ and $\frac{d}{\lambda }=100$. The screen starts from rest and accelerates with $2m/s^2$ at $t=0$. If $C$ is the centre of the line joining $S_1{S}_2$ and meeting the screen, then (Assume $d>>\lambda$)

1. Velocity of the third maxima at $t=3s$ is $6.002m/s$
2. $C$ will always be the central maxima.
3. Fringe Width increases with increase in time.
4. Velocity of third maxima is independent of time.

Q.

In a YDSE both slits produce equal intensities on the screen. A $100\%$ transparent thin film is placed in front of one of the slits. Now the intensity of the geometrical centre of system on the screen becomes $75\%$ of the previous intensity. The wavelength of the light is $6000\stackrel{\circ }{A}$ and ${\mu }_{glass}=1.5$. The thickness of the film cannot be:

1. $0.2\mu m$

2. $1.0\mu m$

3. $1.4\mu m$

4. $1.6\mu m$