Question

Angular width of the first minimum on either side of tge central maximum due to a single slit of width a, illuminated by a light of wave length lambda is......?
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Answer 1

To find:

Angular width of the first minimum on either side of the central maximum due to a single slit of width a, illuminated by a light of wave length $\lambda$

Calculation:

Angular width refers to the angular extent of a particular maxima and minima obtained on the projecting screen.

Let slit width be a , and distance of slit from the projecting screen be D

For the 1st minima:

$\rm{ \therefore \: angular \: width = \dfrac{fringe \: width}{D} }$

$\rm{ = > \: angular \: width = \dfrac{ \beta }{D} }$

$\rm{ = > \: angular \: width = \dfrac{ (\frac{ \lambda D}{a} )}{D} }$

$\rm{ = > \: angular \: width = \dfrac{ \lambda}{a} }$

So , final answer is:

$\blue{ \boxed{ \green{ \sf{ \: angular \: width = \dfrac{ \lambda}{a} }}}}$