Question

In the Young's double slit experiment, the intensities at two points P1 and P2 on the screen are respectively I1 and I2, If P1 is located at the centre of a bright fringe and P2 is located at a distance equal to a quarter of fringe width from P2 then, ratio $\frac{I_1}{I_2}$

• A. $2:1$
• B. $8:1$
• C. $4:1$
• D. $16:1$

Answer 1

The correct option is D $16:1$

Fringe width $\beta =\frac{\lambda D}{d}$
Let the amplitude of that place where constructive inference takes place is a.
The position of fringe at $p_2$ is
$x=\frac{n\lambda D}{d}$
GIven, $\beta =\frac{\beta }{4}$
$\therefore \frac{\lambda D}{4d}=\frac{n\lambda D}{d}$
or $n=\frac{1}{4}$
$\therefore \frac{I_1}{I_2}=\frac{a^2}{{\frac{a}{a}}^2}$
Or $I_1:I_2=16:1$