Answer

Verified

394.8k+ views

**Hint**To solve this question, we need to use the formula for the path difference between two rays emerging from the two slits for the Young’s double slit experiment. By putting the required values from the conditions given in the question into the formula we will get the final answer.

Formula Used: The formula which is used in solving the above question is given by

$ x = \dfrac{{yd}}{D} $ , here $ x $ is the path difference between the rays coming from the two slits of width $ d $ at the point situated at the distance of $ y $ from the centre of the slits on the screen at a distance of $ D $ from the plane of the slits.

**Complete step by step answer**

We represent the situation given in the question by the below diagram.

Since the point P is situated in front of one of the two slits, so we take it to be in from of the upper slit $ {S_1} $ . So, the distance of the point P from the centre of the slit becomes

$ y = \dfrac{d}{2} $ (1)

The two rays originating from the slits meet at the point P. From the above figure, this path difference is given by

$ x = {S_2}P - {S_1}P $

Now, we know that the path difference in the Young’s double slit experiment is given by

$ x = \dfrac{{yd}}{D} $

According to the question, we have $ d = d $ , and $ D = b $ . Putting these we get

$ x = \dfrac{{yd}}{b} $

Finally substituting from (1) we get

$ x = \dfrac{{\left( {d/2} \right)d}}{b} $

$ \Rightarrow x = \dfrac{{{d^2}}}{{2b}} $

Thus we get the path difference for the given double slit experimental setup equal to $ \dfrac{{{d^2}}}{{2b}} $ .

**Hence, the correct answer is option B.**

**Note**

If we do not remember the formula which is used in the above solution to calculate the path difference, then also we can very easily obtain the answer. We just need to have the figure corresponding to the situation given the question from the figure. Then, we have to consider the geometry of that figure to determine the required expression as $ x = {S_2}P - {S_1}P $ .

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Name 10 Living and Non living things class 9 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Write the 6 fundamental rights of India and explain in detail