Question

If Young's apparatus is immersed in water, the effect on fringe width will________

Answer 1

Hint: With the help of the young’s double-slit experiment, the wave nature of the light was proved using the phenomenon of interference. This experiment uses two coherent sources of light. This is placed at a small distance apart which will be slightly greater than the wavelength of the light used. This single beam of light is splitted into the two sources using two slits. This is then made to fall on the screen placed behind.

Complete Step By Step Answer:
The fringe width is defined as the distance between the two consecutive dark or bright fringes.
The fringe width is directly proportional to the distance between the slit and screen and also proportional to the wavelength of the light source but is inversely proportional to the width of the slit.
Mathematically this can be written as,
 $ \Rightarrow \beta = \dfrac{{D\lambda }}{d} $ ……. (1)
Here, $ \beta $ is the fringe width
 $ D $ is slit and screen distance.
 $ \lambda $ is said to be the wavelength of the light source
 $ d $ is the width of the slit.
Given that the whole experiment is immersed in the water.Therefore, we can take the refractive index of water as n. Then we know that,
 $ c = \lambda \nu $ …… (2)
Here, c is the speed of light
 $ \nu $ is said to be the velocity of the light in water.
If we change the medium where the light travels then the frequency remains constant. Therefore, in the above equation, the speed of light will be directly proportional to the wavelength of the light. We know that the speed of the light will be maximum only in the air and vacuum. This means that the speed of the light will definitely be decreased in the water and therefore this, in turn, decreases the wavelength of the light. From equation (1) we know that fringe width is directly proportional to the wavelength of the light. And therefore, if the wavelength decreases the fringe width will become narrower.

Note:
An interference pattern will be obtained in the double-slit experiment. This consists of alternate bright and dark fringes. These fringes are parallel to the slits. The fringe width is constant for all the fringes in the interference pattern. Fringe width is considered to be always independent of the order of fringe. Central bright fringe the fringe formed at the centre of the fringe pattern.