Question

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 wavelength lambda is
(give the correct answer..or your answer will be reported)​

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 wavelength $\lambda$

Calculation:

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

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

For the 1st minima:

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

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

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

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

So, final answer is :

$\red{ \boxed{ \blue{ \rm{\: angular \: width = \dfrac{ \lambda}{a} }}}}$