Question

Two flat mirrors form an angle close to ${180}^{\circ }$ as shown in figure. A source of light S is placed at equal distances b from the mirrors. A screen is at distance a from mirrors. Wavelength of light is $\lambda$ and there is a shield C that block light passing directly to the screen, then

• A. We get bright fringe t A
• B. Fringe width at screen is $\frac{\lambda (a+b)}{4\alpha b}$
• C. Fringe width increases as $\alpha$ increases
• D. Fringe width at screen is $\frac{\lambda a\alpha }{2b}$

Answer 1

Answer: (A), (B)

The correct options are
A We get bright fringe t A
B Fringe width at screen is $\frac{\lambda (a+b)}{4\alpha b}$

From the diagram,

$\sin \alpha =\frac{d/2}{2b}$
$\sin \alpha \simeq \alpha$

$d=4\alpha b$
Since, $\alpha$ is small, $D\simeq a+b$
$w=\frac{\lambda D}{d}=\frac{\lambda (a+b)}{4\alpha b}$

Here $\alpha$ is very small and we get constructive interference at A.