YDSE Problems II

Q.

What is Fresnel Biprism?

Q. A plane glass is kept over a coloured word $\text{VIBGYOR}$, where the colour of letters are the same as the colours of components in white light. The letter which appears least raised is,

1. $\text{R}$
2. $\text{Y}$
3. $\text{O}$
4. $\text{V}$

Q. In Young's double slit interference experiment the wavelength of light used is 6000A. If the path difference between waves reaching a ponit P on the screen is 1.5 microns, then at that point P:

1. second bright band occurs
   
2. third dark band occurs
   
3. second dark band occurs
   
4. thirdbright band occurs

Q.

If yellow light in the Youngs double slit experiment is replaced with a red light, the fringe width will

1. remains unaffected
2. decreases
3. increases
4. first increases then decreases

Q. The intensity of the light from a bulb incident on a surface is $0.22W/m^2$. The amplitude of the magnetic field in this light-wave is $\times 10^{-9} \mathrm{~T}$.(Given:Permittivityofvacuum$\varepsilon_{0}=8.85 \times 10^{-12}C^{2} N^{-1}-m^{-2}$,speedoflightinvacuum$~(c)=3 \times 10^{8}\left.\mathrm{ms}^{-1}\right)$

Q.

In a Young's double slit experiment, the slit separation d is $0.3$ mm and the screen distance D is $1m$. A parallel beam of light of wavelength $600nm$ is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is $11.0$mm. Which of the following statement (s) is/are correct?

1. For $\alpha =0$, there will be constructive interference at point P.

2. For $\alpha =\frac{0.36}{\pi }$ degree, there will be destructive interference at point P.

3. For $\alpha =\frac{0.36}{\pi }$ degree, there will be destructive interference at point O.

4. Fringe spacing depends on $\alpha$.

Q. A prism of refractive index \(n_1\) and another prism of refractive index \(n_2\) are stuck together (as shown in the figure). \(n_1\) and \(n_2\) depend on \(\lambda \), the wavelength of light, according to the relation

\(n_1=1.2+\dfrac{10.8\times 10^{-14}}{\lambda ^2}\) and \(n_2=1.45+\dfrac{1.8\times 10^{-14}}{\lambda ^2}\)

The wavelength for which rays incident at any angle on the interface \(\text{BC}\) pass through without bending at that interface will be _____ \(\text{nm}\)
.

Q. A point source of light is placed at a distance $2\text{m}$ below the surface of a large and deep lake. The fraction of light that escapes directly from water surface will be $({\mu }_{water}=4/3$)

$[$ Absorbtion of light within the water and reflection at surface except where it is total, have been neglected $]$

1. $0.5$
2. $0.3$
3. $0.2$
4. $0.4$

Q. The intensity of central fringe in the interference pattern produced by two identical slits is I. When one of the slits is closed then the intensity at the same point is $I_0$. The relation between I and $I_0$ is

1. $I=4I_0$
2. $I=2I_0$
3. $I=I_0$
4. $I=\frac{I_0}{2}$

Q.

What is the obliquity factor?

Q. A thin film with index of refraction $1.33$ coats a glass lens with index of refraction $1.50$. Which of the following choices is the smallest film thickness that will not reflect light with wavelength $640\text{nm}$ ?

1. $120\text{nm}$
2. $240\text{nm}$
3. $360\text{nm}$
4. $480\text{nm}$

Q. In young’s experiment, the upper slit is covered by a thin glass plate of refractive index $\frac{4}{3}$ and of thickness $9\lambda$, where $\lambda$ is the wavelength of light used in the experiment. The lower slit is also covered by another glass plate of thickness $2\lambda$ and refractive index $\frac{3}{2}$ , as shown in figure. If $I_0$ is the intensity at point P due to slits $S_1$ and $S_2$ each, then :

1. Intensity at point P is $4I_0$
2. Two fringes have been shifted in upward direction after insertion of both the glass plates together.
3. Optical path difference between the waves from $S_1$ and $S_2$ at point P is $2\lambda$.
4. If the source S is shifted upwards by a small distance d2 then the fringe originally at P after inserting the plates, shifts downward by $D\left(\frac{d_2}{d_1}\right)$

Q.

The potential due to charged spherical shell of radius 20 cm at a point 5 cm distance from the center is v the potential on the surface of the spherical shell is.

Q. In an interference pattern the $(n+4{)}^{th}$ blue bright fringe and $n^{th}$ red bright fringe are formed at the same spot. If red and blue light have the wavelength of $7800\AA$ and $5200\AA$, then value of $n$ should be :

Q. Aperture of the human eye is $2\text{mm}.$ Assuming the mean wavelength of light to be $5000\mathring{\text{A}}.$ The angular resolution limit of the eye is nearly

1. $2\text{minute}$
2. $1\text{minute}$
3. $0.5\text{minute}$
4. $1.5\text{minute}$

Q. In an interference pattern ${16}^{th}$ order maximum corresponds to 600nm . What order will be visible if 480nm is used in the same position:

1. 5
2. 10
3. 15
4. 20

Q.

A parallel beam of monochromatic light of wavelenght $\lambda$ is used in a Young's double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. The incident beam makes an angle $\theta =si{n}^{-1}\left(\frac{\lambda }{2d}\right)$ with the normal to the plane of the slits. A transparent sheet of refractive index. ${}^{\prime }{\mu }^{\prime }$ and thickness $t=\frac{\lambda }{2(\mu -1)}$ is introduced infront of one of the slit. Find the intensity at the geometrical centre.

1. 2I

2. 3I

3. 4I

4. I

Q. Two sound waves (expressed in CGS units) given by $y_1=0.3sin\frac{2\pi }{\lambda }(vt-x)$ and $y_2=0.4sin\frac{2\pi }{\lambda }(vt-x+\theta )$ interfere. The resultant amplitude at a place where phase difference is $\frac{\pi }{2}$ will be

1. 0.1 cm
2. 0.5 cm
3. 
4. 0.7 cm

Q. In Young's double slit experiment, the wavelength of light used is doubled and the distance between the two slits is halved, the new fringe width becomes,

1. $\frac{1}{2}\text{times}$
2. $2\text{times}$
3. $3\text{times}$
4. $4\text{times}$

Q.

The box of a pin hole camera, of length I, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$ the spread of the spot (obtained on the opposite wall of the camera) is the sum its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{min}$)when:

1. and

2. and

3. and

4. and

Q. Two soap bubbles of radii 2 cm and 4cm join to form a double bubble in air, then the radius of curvature of interface is 2cm 4cm 23cm 25cm

Q. (a) How is amplitude modulation achieved ?
(b) The frequencies of two side bands in an AM wave are 640 kHz and 660 kHz respectively. Find the frequencies of carrier and modulating signal. What is the bandwidth required for amplitude modulation ?

Q. In Young’s double slit experiment the separation 𝑑 between the slits is $2mm$, the wavelength $\lambda$ of the light used is $5896A^{\circ }$ and distance $D$ between the screen and slits is $100cm$. It is found that the angular width of the fringes is ${0.20}^{\circ }$.To increase the fringe angular width to ${0.21}^{\circ }$ (with same $\lambda$ and $D$) the separation in 𝑚𝑚 between the slits needs to be changed to

Q. White coherent light $(4000-7000\stackrel{\circ }{A})$ is sent through the slits of a YDSE. The separation between the slits is $0.5\text{mm}$ and screen is $50\text{cm}$ away from the slits. There is a hole in the screen at a point 1.0 mm away (along the width of the fringe) from the central line.
a. Which wavelength(s) will be absent in the light coming from the hole?
b. Which wavelength(s) will have a strong intensity?

1. $4000\stackrel{\circ }{A}$, $6000\stackrel{\circ }{A}$.
2. $5000\stackrel{\circ }{A}$, $7000\stackrel{\circ }{A}$
3. $7000\stackrel{\circ }{A}$, $5000\stackrel{\circ }{A}$.
4. $3000\stackrel{\circ }{A}$, $6000\stackrel{\circ }{A}$.

Q. A linear aperture whose width is $0.02\text{cm}$ is placed immediately in front of a lens of focal length $60\text{cm}$. The aperture is illuminated normally by a parallel beam of wavelength $5\times {10}^{-5}\text{cm}$. The distance between the first secondary minima of the diffraction pattern, on either sides of central maxima is

1. $0.30\text{cm}$
2. $0.10\text{cm}$
3. $0.25\text{cm}$
4. $0.20\text{cm}$

Q. The shift of the interference pattern on the screen when the slit is displayed by $Sl=1mm$ along the arc of radius $r$ with centre at $0$.

1. $4mm$
2. $6mm$
3. $10mm$
4. $13mm$

Q. A light wave is incident normally over a slit of width $24\times {10}^{-5}cm$. The angular position of second dark fringe from the central maxima is ${30}^o$. What is wavelength of light?

1. $6000\mathring{A}$
2. $5000\mathring{A}$
3. $3000\mathring{A}$
4. $1500\mathring{A}$

Q. If the monochromatic light is replaced by white light in the double slit experiment, what will happen?

1. No change
2. No fringes are formed
3. A few coloured fringes are found on either side of central white fringe
4. White and dark fringes are only formed

Q. (a) Derive an expression for path difference in Youngs double slit experiment and obtain the conditions for constructive and destructive interference at a point on the screen.
(b) The intensity at the central maxima in Youngs double slit experiment is $I_0$. Find out the intensity at a point where the path difference is $\frac{\lambda }{6},\frac{\lambda }{4}$ and $\frac{\lambda }{3}$.

Q.

White light is used to illuminate the two slits in Young's double slit experiment. The distance between the slits is b and the screen is at a distance d (>> b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

1. $\lambda =\frac{b^2}{3d}$
   

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

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

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