Question 162: Waves Optics

Question

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 $$\mathop A\limits^ \circ  $$ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

Accepted Answer

The slit width is a = 0.1 mm = 10
$$-$$4
m.
The wavelength of the light is $$\lambda$$ = 6000 $$	imes$$ 10
$$-$$10
= 6 $$	imes$$ 10
$$-$$7
.
The distance from the slit to diffraction bands is D = 0.5 m.
We calculate the third dark band from the central band as follows:
$$A\sin 	heta  = 3\lambda  \Rightarrow \sin 	heta  = {{3\lambda } \over a} = {x \over D}$$
$$ \Rightarrow x = {{3\lambda D} \over a} = {{3 	imes 6 	imes {{10}^{ - 7}} 	imes 0.5} \over {{{10}^{ - 4}}}} = 9$$ mm

Answer

3 mm

Answer

9 mm

Answer

4.5 mm

Answer

1.5 mm

Waves Optics

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 $\mathop A\limits^ \circ $ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

Choose the correct answer: