Answer to Question #93806 in Optics for Sridhar

Question

In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern? (a) 0.5 mm (b) 0.02 mm (c) 0.2 mm (d) 0.1 mm

Answer 1

We can write for the central maximum

$\frac {y}{D}=\frac {2λ}{b} (1)$

where b is the width of the central maximum

Using (1) we got

$y=\frac {2λD}{b} (2)$

We can write for for interference pattern

$y=\frac {λD}{d} (3)$

The width of the central maximum is equal to the width of ten maxima

In this case, we can write

$\frac {2λD}{b}=10\frac {λD}{d} (4)$

Using (4) we got

$b=\frac {d}{5} (5)$

b=0.2 mm

Answer

(c) 0.2 mm