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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