Question

In YDSE, the slit widths are in the ratio of $1:9$.The ratio of intensity of the maxima to that of the minima is :

• A. $81:1$
• B. $9:1$
• C. $4:1$
• D. $3:1$

Answer 1

The correct option is C $4:1$

Intensity is proportional to the area of the slit.
As slit widths are in the ratio of $1:9$
The areas are also in the ratio $1:9$
Thus Intensities are in the ratio $1:9$
amplitudes are square root of Intensities
Thus amplitudes are in ratio $1:3$
Let amplitudes be $x$ and $3x$
At maxima the amplitudes get added up $x+3x$
$=4x$
At minima they become $x-3x=-2x$
Intensity of maxima to minima is $\frac{16x^2}{4x^2}=\frac{4}{1}$