Wave Optics

n = tan

When apparatus is immersed in liquid of refractive index , fringe width,

Now

When interference is observed, energy is redistributed.

For dark fringe,
Here,

or,

Here,
At constructive interference position


At destructive interference position,

order minimum in diffraction is given by
Here,

Number of fringes shifted,

or, (for same )

Here,
or,
or,

Angular fringe width is given by Angular fringe width increases when wavelength increases and distance between coherent sources decreases.

Intensity of the bright fringe =
We know, maximum intensity of a bright fringe
Intensity of ligh,t through one slit
Intensity of light through one slit =
Intensity at the point of bright fringe.

Shift in fringe pattern due to introduction of glass plate in the path. of one of slits in Young's.double slit experiment is given by,
Here,


or,
or,
or,

As a thin glass plate is introduced in the path of light from in Young's double slit experiment arrangement, so fringe pattern as a whole is laterally shifted towards .

Doppler shift in wavelength of the light source is given by

For motion away from earth is positive .

Answer (d) one dot rotating about the other stationary dot, sometimes coinciding with it.

Answer (c) Raman effect only

Answer (d)

Let be intensity of incident unpolarised light. Then the intensity of light emerging from the first polaroid will be
Intensity of transmitted light is given by (Malus' law)
where 8 = angle between polaroids.
Now, polaroid is rotated through .
So angle between two polaroids

Percentage of light transmitted through the system,

Width of central maxima,
Given ,


or,
or,

Polarization of wave is possible, if the wave is transverse in nature. Sound wave in air is longitudinal, so it cannot be polarised

Answer (c) 5

The relation between and are,
For small changes in and ,

As
Therefore, using doppler shift

or

In single slit diffraction, the angular width of the central maxima is given by: Where: - is the wavelength of light, - is the slit width. The width of the central maxima is given by: Where is the distance to the screen. Now, if we double the slit width, i.e., becomes , the angular width changes as follows: Since decreases when increases, the corresponding width of the central maxima will also decrease. Hence, the new width will be: Thus, the width of the central maxima is halved when the slit width is doubled.