M1 and M2 are plane mirrors and kept parallel to each other- At point O- there will be a maxima for wavelength - Light from a monochromatic source S of wavelength - is not reaching directly on the screen- Then- - is-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Angular Deviation

M1 and M2 a...

Question

$M_{1}$ and $M_{2}$ are plane mirrors and kept parallel to each other. At point O, there will be a maxima for wavelength $λ$ . Light from a monochromatic source $S$ of wavelength $λ$ is not reaching directly on the screen. Then, $λ$ is:

\frac{{3 d}^{2}}{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{{3 d}^{2}}{2 D}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{d^{2}}{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{{2 d}^{2}}{D}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{{3 d}^{2}}{2 D}$
Light emerging from point S gets reflected from mirrors $M_{1}$ and $M_{2}$ , to interfere constructively at point O.
This means that path difference between light travelling $S M_{1} O$ and $S M_{2} O$ must be $λ$ .
As shown in the figure, path $S M_{1} O = 2 \sqrt{(\frac{D}{2})^{2} + (\frac{d}{2})^{2}}$
path $S M_{2} O = 2 \sqrt{(\frac{D}{2})^{2} + d^{2}}$
$2 \sqrt{(\frac{D}{2})^{2} + d^{2}}$ $-$ $2 \sqrt{(\frac{D}{2})^{2} + (\frac{d}{2})^{2}} = λ$
Thus using Bionomial expansion, $λ$ comes out to be $\frac{3 d^{2}}{2 D}$ .

Suggest Corrections

Similar questions

M_{1}

and

M_{2}

are two plane mirrors which are kept parallel to each other as shown. There is a point

O

on the perpendicular screen just in front of

S .

What should be the wavelength of light coming from monochromatic source

S,

so that a maxima is formed at

O

due to interference of reflected light from both the mirrors. [consider only 1st reflection and

D >> d, d >> λ

]

Q. White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is d and the screen is at a distance

D (>> d)

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 :

Q. Consider the optical system shown in the figure that follows. The point source of light

S

is having wavelength equal to

λ

. The light is reaching screen only after reflection. For point

P

to be

2^{n d}

maxima, the value of

λ

would be

(D >> d

and

d >> λ)

Q. Two point monochromatic and coherent sources of light of wavelength

λ

are placed on the dotted line in front of a large screen. The source emit waves in phase with each other. The distance between

S_{1}

and

S_{2}

^{'} d^{'}

while their distance from the screen is much larger. Then,,
(a) If

d = 7 λ / 2

O

will be minima
(b) If

d = 4.3 λ

, there will be total of

8

minima on y-axis
(c) If

d = 7 λ

O

will be maxima.
(d) If

d = λ

, there will be only one maxima on the screen.
Which is the set of correct statement:

For a parallel beam of monochromatic light of wavelength $^{'} λ^{'}$ , diffraction is produced by a single slit whose width ‘a‘ is of the order of the wavelength of the light. If ‘D‘ is the distance of the screen from the slit, the width of the central maxima will be :

Join BYJU'S Learning Program

M1 and M2 are plane mirrors and kept parallel to each other. At point O, there will be a maxima for wavelength λ. Light from a monochromatic source S of wavelength λ is not reaching directly on the screen. Then, λ is:

$M_{1}$ and $M_{2}$ are plane mirrors and kept parallel to each other. At point O, there will be a maxima for wavelength $λ$ . Light from a monochromatic source $S$ of wavelength $λ$ is not reaching directly on the screen. Then, $λ$ is: