Intensity Amplitude Relationship

Q. 33. Angular width of central maximum in the Fraunhoffer diffraction pattern of a slit is measured. The slit is illuminated by light of wavelength 6000 A.� when the slit is illuminated by the light of another wavelength then the angular width decreases by 30%. Calculate the wavelegth for this light. The same dedcrease in the angular width of central maximum is obtained when the original apparatus is immersed in the liquid. Find the refractive index of the liquid?

Q. In young's double slit experiment , the interference pattern is found to have an intensity ratio between the bright and dark fringes as $9$. This implies that

1. The intensities at the screen due to the two slits are $5$ units and $4$ units respectively.
2. The intensities at the screen due to the slits are $4$ units and $1$ unit respectively.
3. The amplitude ratio is $3$.
4. The amplitude ratio is $2$.

Q. The light of wavelength 600nm is incident normally on a slit of width 3mm . Calculate the angular width of central maximum on a screen kept 3m away from the slit in degree

Q.

In a soccer practice session the football is angle is kept at the centre of the field 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of ${45}^2$ to the horizontal. Will the ball reach the goal post ?

Q. In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed im away, was found to be 0.2^°. What will be the angular width of the first minima, if the entire experimental apparatus immered in water

Q. 101.S1 and S2 are the 2 coherent point sources of light located in the xy plane at pooits (0, 0) and (0, 3 lambda) respectively here lambda is wavelength of light. at which point intensity of interference is maximum. 1)3lambda, 0 2)4 lambda, o 3)5lambda/4, 0 4)2lambda/3, 0

Q.

A light ray falling at an angle of ${45}^{\circ }$ with the surface of a clean slabof ice of thickness 1.00 m is refracted into it at an angle of ${30}^{\circ }$. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum $=3\times {10}^{8}m{s}^{-1}$

Q.

Two coherent sources of intensity ratio $\beta$ interfere. Find the ratio $\frac{[I_{max}-I_{min}]}{[I_{max}+I_{min}]}$ in the interference pattern.

1. $\frac{2\sqrt{\beta }}{[1+\beta ]}$
2. $\frac{2\beta }{[1+\beta ]}$
3. $\left[\frac{(\sqrt{\beta }+1)}{(\sqrt{\beta }-1)}\right]$

4. $\frac{\sqrt{\beta }}{(1+\sqrt{\beta })}$

Q. Use Huygen's principle to show how a plane wavefront propogates from a denser to rarer medium. Hence verify Snell's law of refraction.

Q.

Which of the following functions represent a wave?

1. (x – v t)²

2. $\ln (x–vt)$

3. $e^{-{\left(x-vt\right)}^2}$

4. $\frac{1}{(x+vt)}$

Q. ${\text{M}}_1$ and ${\text{M}}_2$ are two plane mirrors which are kept parallel to each other as shown. There is a point $\text{O}$ on the perpendicular screen just in front of $\text{S}.$ What should be the wavelength of light coming from monochromatic source $\text{S},$ so that a maxima is formed at $\text{O}$ due to interference of reflected light from both the mirrors. [consider only 1st reflection and $D>>d,d>>\lambda$]

1. $\frac{3d^2}{D}$
2. $\frac{3d^2}{2D}$
3. $\frac{d^2}{D}$
4. $\frac{2d^2}{D}$

Q.

If the speed of light Is $3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, Calculate the distance covered by light in $2.00ns$.

Q.

The ratio of the amplitude of the two sources producing interference $3:5$, the ratio of intensities at maxima and minima is

1. $25:6$

2. $5:3$

3. $16:1$

4. $25:9$

Q.

In Young’s double slit experiment, the ratio of maximum to minimum intensities of the fringe system is$4:1$. The amplitudes of the coherent sources are in the ratio:

1. $4:1$

2. $3:1$

3. $2:1$

4. $1:1$

Q. 31. Distance between the slits, in YDSE, shown in figure is d=20?, where ? is the wavelength of light used. Find the angle ? , where :- 1. Central maxima (where path difference is zero) is obtained. 2. third order maxima is obtained.

Q. X-rays of wavelength 22 pm are scatered from a carbon target at an angle of 85 to the incident beamThe Compton shit for X-rays is (cos 850.088)

Q. two coherent light sources each of wavelength lambda are separated by a dis†an ce 3 lambda.The total number of minima formed on line AB which runs from -infinity to +infinity is

Q.

The ratio of angular dispersion of to the angle of deviation for the mean wavelength is called Dispersive Power. Represented by

1. 

2. 

3. 

4. 

Q. A monochromatic parallel beam of light of wavelength $\lambda$ is incident normally on the plane containing slits $S_1$ and $S_2$. The slits are of unequal width such that intensity only due to one slit on screen is four times that only due to the other slit. The screen is placed along y-axis as shown. The distance between slits is $d$ and that between screen and slit is $D$. Match the statements in column-I with results in column-II.


$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \begin{array}{c}\text{(A)The distance between two points on screen having equal}\\ \text{intensities, such that intensity at those points is}(\frac{1}{9}{)}^{th}\text{of maximum intensity.}\end{array}& \text{(p)}\frac{D\lambda }{3d}\\ \begin{array}{c}\text{(B)The distance between two points on screen having equal}\\ \text{intensities, such that intensity at those points is}(\frac{3}{9}{)}^{th}\text{of maximum intensity.}\end{array}& \text{(q)}\frac{D\lambda }{d}\\ \begin{array}{c}\text{(C)The distance between two points on screen having equal}\\ \text{intensities, such that intensity at those points is}(\frac{5}{9}{)}^{th}\text{of maximum intensity.}\end{array}& \text{(r)}\frac{2\lambda D}{d}\\ \begin{array}{c}\text{(D)The distance between two points on screen having equal}\\ \text{intensities, such that intensity at those points is (}\frac{7}{9}{)}^{th}\text{of maximum intensity.}\end{array}& \text{(s)}\frac{3\lambda D}{d}\\ & \text{(t)}\frac{2\lambda D}{3d}\end{array}$

1. $A–q,s,B–q,r,s,C–q,t,D–p,r,s$
2. $A–q,r,s,B–p,q,r,s,tC–q,r,s,D–p,q,r,s,t$
3. $A–q,s,B–q,r,s,C–q,r,tD–p,r,s$
4. $A–p,s,t,B–p,r,s,C–q,s,D–p,r,s$

Q. Light of wavelength 589.3 nm is incident normally on a slit of width 0.01mm. The angular width of the central diffraction maximum at a distance of 1m from the slit, is 1) 0.68 ^° 2) 0.34 ^° 3) 2.05 ^° 4) 6.75 ^°

Q. A particle executing SHM with amplitude A has maximum velocity $v_0$. Its speed at displacement $\frac{A}{\sqrt{2}}$ will be

1. $\frac{v_0}{\sqrt{2}}$
2. $v_0$
3. Zero
4. $\frac{v_0}{\sqrt{3}}$

Q. Assume that light of wavelength 6000 A⁰ is coming from a star . What is the limit of resolution of a telescope whose objective has diameter of 100 inch

Q. Beams of red, green and violet light are falling on the refracting face of a thin prism, all at same angle of incidence. If their angles of deviation are ${\theta }_1,{\theta }_2$ and ${\theta }_3$ respectively, then

1. ${\theta }_1={\theta }_2={\theta }_3$
2. ${\theta }_1<{\theta }_2<{\theta }_3$
3. ${\theta }_1>{\theta }_2>{\theta }_3$
4. ${\theta }_2>{\theta }_1>{\theta }_3$

Q. The two interfering waves have intensities in the ratio 9 : 4. The ratio of intensities of maxima and minima in the interference pattern will be

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

Q. 34.In YDSE how many maxima can be obtained on the screen if the wavelength of light used is 200nm and d=700nm:- 1)12 2)7 3)18 4)14

Q.

What is Huygenss principle?

Q. Light of wavelength 2×10^{-3}m falls on a slit of width 4×10^{-3}m .Find angular dispersion of cental maximum

Q.

A mica strip and a polystyrene strip are fitted on the two slits of a double-slit apparatus. The thickness of the strips is 0.50 mm and the separation between the slits is 0.12 cm. The refractive index of mica and polystyrene are 1.58 and 1.55 respectively for the light of wavelength 590 nm which is used in the experiment. The interference is observed on a screen a distance of one meter away. (a) What would be the fringe width? (b) At what distance from the centre will the first maximum be located?

Q. a parallel beam of light of wavelength 600nm is incident normally on a slit of width a if the distance between the slits and screen is 0.8 m and the distance of second order maximum from the centre of the screen is 15mm, calculate the width of slit.

Q. In an interference pattern produced by two identical slits, the intensity at the site of the central maximum is I.
The intensity at the same spot when either of the two slits is closed is $I_0$. We must have

1. $I_{=}{I}_0$
   
2. $I_{=}2I_0$
   
3. $I_{=}4I_0$
   
4. $Iand{I}_0$ are not related