Wave Optics Test

Result

Wave Optics Test - 75

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Question 1
1 / -0

A thin slice is cut of glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate with the curved sirface sownwards. Monochromatic light is incident normally from the top. the observed interfernce fringes from the combination do not follow on of the following staements.

A
The frings are straight and parallel to the length of the pleace.

B
The line of contract of the cylindrical glass piece and the glass plate appears dark.

C
The fring spacing increases as we go outwards

D
The frings are fomed due to the interference of light rays reflected from the curved surface of the cylindrical place and the top surfce of the glass plate.

Solution
Question 2
1 / -0

Two slits in Young's double-slit experiment have widths in the ratio 9 : 4.Find the ratio of light intensities at maxima and minima in the interference pattern:

A
25:16

B
25:1

C
5:1

D
5:16

Solution

Given,
$$\frac { { I }_{ 1 } }{ { I }_{ 2 } } =\frac { { W }_{ 1 } }{ { W }_{ 2 } } =\frac { 9}{ 4 } $$
We know that Width is directly proportional to intensity
Therefore,
$$\frac { { I }_{ max } }{ { I }_{ min } } =\frac { { \left( \sqrt { { I }_{ 2 } } +\sqrt { { I }_{ 1 } } \right) }^{ 2 } }{ { \left( \sqrt { { I }_{ 2 } } -\sqrt { { I }_{ 1 } } \right) }^{ 2 } } ={ \left[ \frac { \sqrt { \frac { { I }_{ 2 } }{ { I }_{ 1 } } } +1 }{ \sqrt { \frac { { { I }_{ 2 } } }{ { I }_{ 1 } } } -1 } \right] }^{ 2 }$$
Substitute all value in above equation
$$\frac { { I }_{ max } }{ { I }_{ min } } ={ \left[ \frac { \sqrt { \frac { 4 }{ 9 } } +1 }{ \sqrt { \frac { { 4 } }{ 9 } } -1 } \right] }^{ 2 }\\ \quad \quad \quad \quad ={ \left[ \frac { 2+3 }{ 2-3 } \right] }^{ 2 }\\ \quad \quad \quad \quad ={ \left[ \frac { 5 }{ -1 } \right] }^{ 2 }=\frac { 25 }{ 1 } =25:1 $$
Option B is correct option
Question 3
1 / -0

In the figure shown if a particle beam of white light is incident on the plane of the slits then the distance of the white spot on the screen from$$O$$ is [Assume $$d < < D,\lambda < < d$$ ]

A
$$0$$

B
$$d/2$$

C
$$d/3$$

D
$$d/6$$

Solution
Question 4
1 / -0

In $$YDSE,d=2\ mm,D=2\ m$$ and $$\lambda=500\ nm$$. If intensity of two slits are $$l_{0}$$ and $$9l_{0}$$ then find intensity at $$y=\dfrac {1}{6}\ mm$$.

A
$$7l_{0}$$

B
$$10l_{0}$$

C
$$16l_{0}$$

D
$$4l_{0}$$

Solution
Question 5
1 / -0

Intensity of central fringe in interference pattern is $$0.1 W/m^2$$ then find intensity at a point having path difference $$\lambda /3$$ on screen from centre ( in $$m W /m^2$$) :

A
$$2.5$$

B
$$5$$

C
$$7.5$$

D
$$10$$

Solution

Given that $$I_c=0.1$$$$w/m^2$$ be the intensify of centrical bright fringe.
Now intensity at any point with phase & is given by
$$I=4I_o\cos^2\phi/2$$$$\{I_o=$$ intensity of light$$\}$$
Now, at central bright fringe $$\phi =0, I=I_c$$
$$=I_c=4I_o\cos^20$$

$$=\dfrac{0.1}{4}=I_o$$
Now at path difference $$\Delta x=\dfrac{\lambda}{3}$$

as we know $$\phi =k\Delta x$$
& $$k=\dfrac{2\pi}{\lambda}=$$ angular wave number

$$\phi =\dfrac{2\pi}{\lambda}\times \dfrac{\lambda}{3}=\dfrac{2\pi}{3}$$

$$I=4I_o\cos^2\left(\dfrac{2\pi/3}{2}\right)$$

$$\Rightarrow I=4\times \dfrac{0.1}{4}\times \dfrac{1}{4}=0.025 w/m^2$$

$$I=2.5m W/m^2$$.
Question 6
1 / -0

If the ratio of the intensity of two coherent source s is $$4$$ then the visibility $$[( I_{max} -I_{min} )/ ( I_{ max} + I_{min} ) ]$$ of the fringes is

A
$$4$$

B
$$4/5$$

C
$$3/5$$

D
$$9$$

Solution
Question 7
1 / -0

If in a Young's double slit experiment, the slit distance is $$3\ cm$$, the separation between slits and screen is $$70cm$$ and wavelength of light is $$1000\ A^{o}$$, then fringe width will be $$(\alpha=1^{o}, \mu=1.5)$$

A
$$2\times 10^{-5}$$

B
$$2\times 10^{-3}$$

C
$$0.2\times 10^{-3}$$

D
$$none\ of\ these$$
Question 8
1 / -0

White light containg radiations of wevelenght $$420nm$$ to $$700 nm$$ is used in a Youngs double slit experiment as shown in figure. Which wavelength is completely absent at $$p$$?

A
$$500 nm$$

B
$$667 nm$$

C
$$600 nm$$

D
All of these

Solution
Question 9
1 / -0

In a $$YDSE,$$ $$\lambda = 6000\mathop A\limits^0 ,$$ $$D=2m,$$ $$d=6mm,$$ when a film of refractive index $$1.5$$ is introduced in front of the lower slit$$,$$ the third maxima shifts to the origin. Find the thickness of the film. Find the position of the fourth maxima.

A
$$3\mu m, - 1.2mm$$

B
$$3.6\mu m, - 1.4mm$$

C
$$3.6\mu m,0.2mm$$

D
$$4\mu m,1.7mm$$

Solution
Question 10
1 / -0

In a double slit experiment, sodium light of wavelength 589 nm produces fringes spaced 1.8 mm on a screen. If the source is replaced by another one of wavelength 436 nm the fringe spacing is :

A
1.33 mm

B
2.3 mm

C
0.33 mm

D
2 mm

Solution