Wave Optics Test

Result

Wave Optics Test - 51

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Weekly Quiz Competition

Question 1
1 / -0

Light of wavelength $$600$$ is incident on a single slit. The first minimum of the diffraction pattern is obtained pattern is obtained at a distance of 4 from the center. The distance between the screen and the slit is 2m. What is the width of slit?

A
0.2 m

B
0.3 m

C
0.5 m

D
0.6 m

Solution
Question 2
1 / -0

In a Young's double slit experiment, constructive interference is produced at a certain point $$P$$. The intensities of light at $$P$$ due to the individual sources are $$4$$ and $$9$$ units. The resultant intensity at point $$P$$ will be-

A
$$13$$ units

B
$$25$$ units

C
$$\sqrt{97}$$ units

D
$$5$$ units

Solution

$$I_t = \left(\sqrt{I}_1 + \sqrt{I}_2\right)^2$$
$$= (2 + 3)^2$$
$$= 25$$
Question 3
1 / -0

When waves of same intensity from two coherent sources reach a point with zero path different the resulting intensity is K . When the above path difference is $$\lambda /4$$ the intensity becomes

A
K

B
K/2

C
K/4

D
K/8

Solution

The maximum intensity is formed at $$\Delta x=0$$ which is $$k$$
Intensity at any other point having path difference $$\Delta x$$ is given by
$$k'=k\cos ^{ 2 }{ \left( \cfrac { \pi }{ \lambda } \Delta x \right) } $$
For $$\Delta x=\cfrac{\lambda}{4}$$, $$\cfrac{\pi}{\lambda}.\Delta x=\frac{\pi}{4}$$ so
$$k'=k\cos ^{ 2 }{ \left( \cfrac { \pi }{ 4 } \right) } =\cfrac{k}{4}$$
Question 4
1 / -0

The wavelength of characteristic $$X \text { -ray } K _ { \alpha }$$ a line emitted by hydrogen like atom is $$0.32 \mathrm { A } ^{ \circ }$$. The wavelength of $$K _ { \beta }$$ line emitted by the same element is

A
$$0.21 { \mathrm { A } }$$

B
$$0.27 \mathrm { A }$$

C
$$0.33 \mathrm { A }$$

D
$$0.40 \hat { \mathrm { A } }$$
Question 5
1 / -0

$$ s_1 $$ and $$s_1 $$ are two sources of sound emitting sine waves. The two sporces are in phase. The source emittied by the two sources interfere at point F. The waves of wavelength:

A
1 m will result in constructive interference

B
$$ \frac { 2 }{ 3 } m $$ will result in constructive interference

C
2 m will result in destructive interference

D
4 m will result in destructive interference

Solution

We know that,

For constructive

Path difference = $$n λ$$

$$ {{S}_{1}}F-{{S}_{2}}F=n\lambda $$

$$ 6m-4m=n\lambda $$

$$ 2\,m=n\lambda $$

$$ \lambda =\dfrac{n}{2}\,m $$

Where, $$n= 0, 1, 2….$$

So, $$\lambda =0,0.5\,m,1\,m,\dfrac{3}{2}\,m,2\,m....$$

Hence, the wave length is $$1\ m$$ in constructive interference
Question 6
1 / -0

In the ideal YDSE when a glass plate $$(RI= 1.5)$$ of thickness t is introduced in path of one of interfering beams , the intensity at the position where central maximum occurred previously remains unchanged. The minimum thickness of glass plate is :

A
$$\lambda$$

B
$$3\lambda$$

C
$$4\lambda$$

D
$$2\lambda$$

Solution

$$\begin{array}{l} Shift=\frac { D }{ d } \left( { \mu -1 } \right) t \\ =\frac { { D\lambda } }{ d } \\ \Rightarrow t=\frac { \lambda }{ { \mu -1 } } =2\lambda \\ Hence, \\ option\, \, D\, \, correct\, \, answer. \end{array}$$
Question 7
1 / -0

The velocity of a moving galaxy is $$300 km s^{-1}$$ and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as 0.5 nm. Then, the actual wavelength of the spectral line is

A
$$3000 A^{o}$$

B
$$5000 A^{o}$$

C
$$6000 A^{o}$$

D
$$4500 A^{o}$$

Solution
Question 8
1 / -0

In Young's double slit experiment $$10th$$ order maxima is obtained at the point of observation in the interference pattern for $$\lambda = 7000 A^o$$. If the source is replaced by another one of wavelength $$5000\ A^o$$ then the order of maximum at the same point will be

A
$$12\ th$$

B
$$14\ th$$

C
$$16\ th$$

D
$$18\ th$$

Solution
Question 9
1 / -0

Fringe width will be more wide for which color?

A
Red

B
Green

C
Yellow

D
blue

Solution

Solution: As Fringe width is directly proportional to the wavelength, so more the wavelength more will be the width.
Since the red colour among the VIBGYOR has the highest wavelength therefore the Fringe width will be highest for the red.
Hence, the correct option is (A).
Question 10
1 / -0

A monochromatic light is incident on a single slit of width $$24\times 10^{-5}\ cm$$. Calculate wavelength of light if angular position of $$1^{st}$$ secondary maxima is $$30^{o}$$.

A
$$8000\ A^{o}$$

B
$$12000\ A^{o}$$

C
$$6000\ A^{o}$$

D
$$16000\ A^{o}$$

Solution