Question 414: Wave Optics

Question

In a diffraction pattern due to a single slit of width $a$,  the first minimum is observed at an angle 30
o
when light of wavelength 5000 $\mathop A\limits^ \circ  $ is incident on the slit. The first secondary maximum is observed at an angle of

Accepted Answer

For the first minima, the path difference between extreme waves
sin $	heta $ = ${\lambda  \over a}$
$ \Rightarrow $ ${1 \over 2}$ = ${\lambda  \over a}$
$ \Rightarrow $ $a$ = 2$\lambda $
For first secondary maximum, the path difference between extreme waves
$\sin 	heta ' = {{3\lambda } \over {2a}}$ = ${3 \over 2}\left( {{1 \over 2}} ight)$
$ \Rightarrow $ $	heta '$ = ${\sin ^{ - 1}}\left( {{3 \over 4}} ight)$

Answer

sin
$-$1
$\left( {{1 \over 2}} \right)$

Answer

${\sin ^{ - 1}}\left( {{3 \over 4}} \right)$

Answer

${\sin ^{ - 1}}\left( {{1 \over 4}} \right)$

Answer

${\sin ^{ - 1}}\left( {{2 \over 3}} \right)$

Wave Optics

In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle 30 o when light of wavelength 5000 \mathop A\limits^ \circ is incident on the slit. The first secondary maximum is observed at an angle of

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