Question

Find the angular fringe width in Young's double-slit experiment with a blue-green light of wavelength $ 6000{A^\circ } $ . The separation between the slits is $ 3.0 \times {10^{ - 3}}m $ .

Answer 1

Hint : We will start our solution by understanding the term angular fringe. The angular fringe describes the separation between the fringes. Now to solve this question we will use the formula width of angular fringe which gives the relationship between the separation between the two slits and wavelengths which are provided in the question.

Formula used:
 $ \Rightarrow \theta = \dfrac{\lambda }{d} $ ,
where $ \lambda $ is wavelength and $ d $ is a separation between the slits.

Complete step by step answer
Starting from the young’s double slits experiment which is used to observe the interference of light. Young’s experiment can be used to determine the wave behavior of light.
From the young’s double slits experiment angular fringe width is given as $ \theta $ which can be given as
 $ \Rightarrow \theta = \dfrac{\lambda }{d} $ ---------------- Equation $ (1) $
Where $ \lambda $ the wavelength of blue-green is light and $ d $ is a separation between the slits.
As the wavelength is given which is
 $ \Rightarrow \lambda = 6000{A^\circ } = 6 \times {10^{ - 10}}m $ ,
 separation $ d = 3.0 \times {10^{ - 3}}m $
Now putting the values of $ \lambda $ and $ d $ in Equation $ (1) $ we get easily get the value of angular fringe $ \theta $
 $ \Rightarrow \theta = \dfrac{{6 \times {{10}^{ - 10}}m}}{{3.0 \times {{10}^{ - 3}}m}} $
 $ \Rightarrow \theta = 2 \times {10^{ - 4}} $
So the angular fringe can be given as $ \theta = 2 \times {10^{ - 4}} $ which can also be given as below
 $ \Rightarrow\theta = {0.0002^\circ } $
Hence the angular fringe width of the blue-green light of wavelength $ \lambda = 6000{A^\circ } $ and the separation $ d = 3.0 \times {10^{ - 3}}m $ by using young’s double-slit experiment is $ \theta = {0.0002^\circ } $ .

Note
It has to be noted that here the angular fringe width is in degree not in radian. We can also obtain the answer in radian by multiplying the answer by $ \dfrac{\pi }{{{{180}^\circ }}} $ . Also from the formula of the double-slit experiment, we can show that the angular fringe is directly proportional to the wavelength of light and inversely proportional to the distance between two slits.