Question

The point S is monochromatic source of light emitting light of wavelength $\lambda .$ At the point P at a distance x from the mirror as shown in the figure, interference takes place between two light rays one directly coming from source S and another after reflection from the mirror such that a maxima is formed. The value of x may be:

• A. $120\lambda$
• B. $125\lambda$
• C. $62.5\lambda$
• D. $187.5\lambda$

Answer 1

Answer: (C), (D)

$187.5\lambda$

$\Delta x=(SA+AP)-SP$
$=(SA+AB)-SP$
$=+SB-SP$
$=500x[\sqrt{1+\frac{9}{{500}^2}}-\sqrt{1+\frac{1}{{500}^2}}]$

$=500x[(1+\frac{9}{2\times {500}^2})-(1+\frac{1}{2\times {500}^2})]$
$=\frac{500x}{2\times {500}^2}\left[8\right]=\frac{\lambda }{2},\frac{3\lambda }{2}.......$
$x=62.5\lambda ,187.5\lambda .......$