Question 225: Wave Optics

Question

A Young's double-slit experiment is performed using monochromatic light of wavelength $$\lambda $$. The
intensity of light at a point on the screen, where the path difference is $$\lambda $$, is K units. The intensity
of light at a point where the path difference is $${\lambda  \over 6}$$ is given by $${{nK} \over {12}}$$, where n is an integer. The value
of n is __________.

Accepted Answer

From 1
st
case,
$$\Delta $$$$\phi $$ = $${{2\pi } \over \lambda } 	imes \lambda $$ = 2$$\pi $$
$$ 	herefore $$ I
net
= 4Icos
2
$${{\Delta \phi } \over 2}$$ = 4I = K (Given)
From 2
nd
case,
$$\Delta $$$$\phi $$ = $${{2\pi } \over \lambda } 	imes {\lambda  \over 6}$$ = $${\pi  \over 3}$$
$$ 	herefore $$ I
net
= 4I cos
2
$${{\Delta \phi } \over 2}$$
= 4I $$ 	imes $$ $${3 \over 4}$$ = $${3 \over 4}K$$
$$ 	herefore $$ According to question,
$${{nK} \over {12}}$$ = $${3 \over 4}K$$
$$ \Rightarrow $$ n = 9

Wave Optics

Integer / Numeric Answer Type