1.

(a) In Illustration 2.20, how many dark rings will be observed on the wall? (b) What is the Path difference at point P?

Answer»

Solution :(a) Path DIFFERENCE corresponding to minima in our given range is `lambda//2, 3 lambda//2, 5 lambda//2`.
Hence, three dark rings will be observed on the wall.
(b) Path difference between the waves reaching at P,
from Fig. 2.20 `Delta x = S_(2) A`
`S_(2) P - S_(1) P = Delta x or d cos theta = Delta x`
`cos theta = (Delta x)/(d)`
But `TAN theta = (y)/(D)`
`IMPLIES cos theta = (sqrt(D ^(2) - Y^(2)))/(D)`
`(D sqrt(1 - (y^(2))/(D^(2))))/(D)`
`= (1 - (y^(2))/(D^(2)))^(1//2) = (1 - (Y^(2))/(2D^(2)))`
From (i) `Delta x = d cos theta = d (1-(y^(2))/(2D^(2)))`
From (i) and (ii), we can find the RADIUS of any dark of bright ring.


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